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</a></div></div><div class="external-links-container"><ul class="profile-links new-profile js-UserInfo-social"><li class="profile-profiles js-social-profiles-container"><i class="fa fa-spin fa-spinner"></i></li></ul></div></div></div><div class="right-panel-container"><div class="user-content-wrapper"><div class="uploads-container" id="social-redesign-work-container"><div class="upload-header"><h2 class="ds2-5-heading-sans-serif-xs">Uploads</h2></div><div class="documents-container backbone-social-profile-documents" style="width: 100%;"><div class="u-taCenter"></div><div class="profile--tab_content_container js-tab-pane tab-pane active" id="all"><div class="profile--tab_heading_container js-section-heading" data-section="Papers" id="Papers"><h3 class="profile--tab_heading_container">Papers by Hun Hee Lee</h3></div><div class="js-work-strip profile--work_container" data-work-id="116584437"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/116584437/Beurling_Fourier_algebras_on_Lie_groups_and_their_spectra"><img alt="Research paper thumbnail of Beurling-Fourier algebras on Lie groups and their spectra" class="work-thumbnail" src="https://attachments.academia-assets.com/112673834/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/116584437/Beurling_Fourier_algebras_on_Lie_groups_and_their_spectra">Beurling-Fourier algebras on Lie groups and their spectra</a></div><div class="wp-workCard_item"><span>Advances in Mathematics</span><span>, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU (n), the Heisenberg group H, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover E(2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate "polynomially growing" weights does not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. CONTENTS 1. Introduction 2 1.1. Basic strategy 4 1.2. Organization 6 2. Preliminaries 6 2.1. Unbounded operators 6 2.1.1. Tensor products 8 2.1.2. Homomorphisms 8 2.1.3. Homomorphisms for non-commuting pairs 9 2.2. Lie groups, Lie algebras and related operators 9 2.3. Complexification of Lie groups 9 2.3.1. Operators associated to certain elements of the universal enveloping algebra and entire vectors 10 2.3.2. The choice of Fourier transforms 13 3. A refined definition for Beurling-Fourier algebras 13 3.1. Motivation: review of weights on abelian groups 13 3.2. Weights on the dual of G and Beurling-Fourier algebras 14 3.2.1. When W is bounded below 18 3.2.2. When G is separable and type I 19 3.3. Examples of weights 20 3.3.1. A list of weight functions on R k × Z n−k 20 3.3.2. Central weights 21 3.3.3. Extension from closed subgroups 23</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="097d0675385186b0484a7698b2b24831" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112673834,"asset_id":116584437,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112673834/download_file?st=MTczMzkwMzc1MCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="116584437"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="116584437"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116584437; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116584437]").text(description); $(".js-view-count[data-work-id=116584437]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116584437; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116584437']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 116584437, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "097d0675385186b0484a7698b2b24831" } } $('.js-work-strip[data-work-id=116584437]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116584437,"title":"Beurling-Fourier algebras on Lie groups and their spectra","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU (n), the Heisenberg group H, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover E(2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate \"polynomially growing\" weights does not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. CONTENTS 1. Introduction 2 1.1. Basic strategy 4 1.2. Organization 6 2. Preliminaries 6 2.1. Unbounded operators 6 2.1.1. Tensor products 8 2.1.2. Homomorphisms 8 2.1.3. Homomorphisms for non-commuting pairs 9 2.2. Lie groups, Lie algebras and related operators 9 2.3. Complexification of Lie groups 9 2.3.1. Operators associated to certain elements of the universal enveloping algebra and entire vectors 10 2.3.2. The choice of Fourier transforms 13 3. A refined definition for Beurling-Fourier algebras 13 3.1. Motivation: review of weights on abelian groups 13 3.2. Weights on the dual of G and Beurling-Fourier algebras 14 3.2.1. When W is bounded below 18 3.2.2. When G is separable and type I 19 3.3. Examples of weights 20 3.3.1. A list of weight functions on R k × Z n−k 20 3.3.2. Central weights 21 3.3.3. 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Lie groups, Lie algebras and related operators 9 2.3. Complexification of Lie groups 9 2.3.1. Operators associated to certain elements of the universal enveloping algebra and entire vectors 10 2.3.2. The choice of Fourier transforms 13 3. A refined definition for Beurling-Fourier algebras 13 3.1. Motivation: review of weights on abelian groups 13 3.2. Weights on the dual of G and Beurling-Fourier algebras 14 3.2.1. When W is bounded below 18 3.2.2. When G is separable and type I 19 3.3. Examples of weights 20 3.3.1. A list of weight functions on R k × Z n−k 20 3.3.2. Central weights 21 3.3.3. 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The question of when a weighted Fourier algebra on G G ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G G be a compact connected Lie group. The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of the Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d1192d6bdf37e678757263ec4c63ed9b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112673808,"asset_id":116584436,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112673808/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="116584436"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="116584436"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116584436; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116584436]").text(description); $(".js-view-count[data-work-id=116584436]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116584436; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116584436']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 116584436, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d1192d6bdf37e678757263ec4c63ed9b" } } $('.js-work-strip[data-work-id=116584436]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116584436,"title":"Some Beurling–Fourier algebras on compact groups are operator algebras","translated_title":"","metadata":{"abstract":"Let G G be a compact connected Lie group. The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of the Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.","publisher":"American Mathematical Society (AMS)","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Transactions of the American Mathematical Society"},"translated_abstract":"Let G G be a compact connected Lie group. The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of the Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.","internal_url":"https://www.academia.edu/116584436/Some_Beurling_Fourier_algebras_on_compact_groups_are_operator_algebras","translated_internal_url":"","created_at":"2024-03-23T02:38:08.157-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112673808,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673808/thumbnails/1.jpg","file_name":"S0002-9947-2015-06653-7.pdf","download_url":"https://www.academia.edu/attachments/112673808/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Beurling_Fourier_algebras_on_compac.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673808/S0002-9947-2015-06653-7-libre.pdf?1711188579=\u0026response-content-disposition=attachment%3B+filename%3DSome_Beurling_Fourier_algebras_on_compac.pdf\u0026Expires=1733907351\u0026Signature=GuoIuJQPxyHcWtjewQJh4cnOPCoF5jCmrjDM7Ml7opNE2b-9-ccdTTOn5wPQImMUaQOa7zAvRMCd3wj1VH1PEnpMQXfIQ0YH3beE2z42UFX1~v0OZZ5wJYmx66Zjk92qUADWXLN3SLHw2t25h7dz~BSLoTDklsCe0n8ulgA1ZthB0968UNE5e9YY7vdQTuN~SrxpaIrwHGaz0oVDfARS85HT0vwoXWGNJhuFTRx52x1cFal0lWkD1nJIqWsEAUh-cMtATsB3a3dZlURYjNMp~MuD1LkNfrNmT98jvJxAOv9ebmT9jj~jZGyOn0EZf1S3VhtcYTKE3ES8J~~r73Ppqg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Some_Beurling_Fourier_algebras_on_compact_groups_are_operator_algebras","translated_slug":"","page_count":31,"language":"en","content_type":"Work","summary":"Let G G be a compact connected Lie group. The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of the Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":112673808,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673808/thumbnails/1.jpg","file_name":"S0002-9947-2015-06653-7.pdf","download_url":"https://www.academia.edu/attachments/112673808/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Beurling_Fourier_algebras_on_compac.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673808/S0002-9947-2015-06653-7-libre.pdf?1711188579=\u0026response-content-disposition=attachment%3B+filename%3DSome_Beurling_Fourier_algebras_on_compac.pdf\u0026Expires=1733907351\u0026Signature=GuoIuJQPxyHcWtjewQJh4cnOPCoF5jCmrjDM7Ml7opNE2b-9-ccdTTOn5wPQImMUaQOa7zAvRMCd3wj1VH1PEnpMQXfIQ0YH3beE2z42UFX1~v0OZZ5wJYmx66Zjk92qUADWXLN3SLHw2t25h7dz~BSLoTDklsCe0n8ulgA1ZthB0968UNE5e9YY7vdQTuN~SrxpaIrwHGaz0oVDfARS85HT0vwoXWGNJhuFTRx52x1cFal0lWkD1nJIqWsEAUh-cMtATsB3a3dZlURYjNMp~MuD1LkNfrNmT98jvJxAOv9ebmT9jj~jZGyOn0EZf1S3VhtcYTKE3ES8J~~r73Ppqg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112673809,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673809/thumbnails/1.jpg","file_name":"S0002-9947-2015-06653-7.pdf","download_url":"https://www.academia.edu/attachments/112673809/download_file","bulk_download_file_name":"Some_Beurling_Fourier_algebras_on_compac.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673809/S0002-9947-2015-06653-7-libre.pdf?1711188581=\u0026response-content-disposition=attachment%3B+filename%3DSome_Beurling_Fourier_algebras_on_compac.pdf\u0026Expires=1733907351\u0026Signature=HBCCeRpveHIACDxcFQt4-nijTpL3M7AJPrQxnl1US~S1fmLbh112xZyeV2-8zBJ~~TdJDUeO2kgwow~6lHORuMoW2vaHPiB0NvjGPa0XtXHNW47M6H5XeWVC98WlctWlR4MZPSIV-GSQHfkFE-~xqeEIU5UAMYtzbT64iMUDSwfza9Kwm5XpADlla91amlChhFcBWXenb~s2mS0m-qyIFX4eVS7BvzelwOJziczEHxVaRSFBztzmNI8CO~1zHqryGuJpFHAXfH8gtlSKZkL7bLF5JNAK17fQ-vwC7y6xkLEnVjKN4n6uu4gICkQKEjrEjwB8oq~ceal3X9R7eYmIAQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":26817,"name":"Algorithm","url":"https://www.academia.edu/Documents/in/Algorithm"},{"id":38072,"name":"Annotation","url":"https://www.academia.edu/Documents/in/Annotation"}],"urls":[{"id":40541368,"url":"http://www.ams.org/tran/2015-367-10/S0002-9947-2015-06653-7/S0002-9947-2015-06653-7.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116584430"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/116584430/Corrigendum_Similarity_degree_of_Fourier_algebras"><img alt="Research paper thumbnail of Corrigendum: Similarity degree of Fourier algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/112673830/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/116584430/Corrigendum_Similarity_degree_of_Fourier_algebras">Corrigendum: Similarity degree of Fourier algebras</a></div><div class="wp-workCard_item"><span>Journal of Functional Analysis</span><span>, 2018</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes the matricial open unit ball b 1 (M n ⊗ V 0) onto b 1 (M n ⊗ [V 0 /(V 0 ∩ W)]) ∼ = b 1 ([M n ⊗ V 0 ]/[M n ⊗ (V 0 ∩ W)]). We now recall the notation of [7]. For a Banach algebra and operator space A, c ≥ 1, A c (contained in B(H c)) is the universal operator algebra generated by representations on Hilbert spaces π : A → B(H) with completely bounded norm π cb ≤ c, and ι c : A → A c is the canonical embedding. Note that we assume that ι 1 is injective. We say that A satisfies the similarity property for completely bounded homomorphims if for each completely bounded homomorphim π : A → B(H), there is an invertible S in B(H) for which Sπ(•)S −1 cb ≤ 1. We also consider the "weighted multiplication" map on the N-fold Haagerup tensor product of A with itself, m N,c : A N ⊗ h → A c , given on elementary tensor by m N,c (u 1 ⊗ • • • ⊗ u N) = 1 c N ι c (u 1). .. ι c (u n) = 1 c N ι c (u 1 ,. .. u N) which is a complete contraction.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9d5648fc1e191a3f869a575b799d2225" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112673830,"asset_id":116584430,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112673830/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="116584430"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="116584430"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116584430; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116584430]").text(description); $(".js-view-count[data-work-id=116584430]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116584430; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116584430']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 116584430, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "9d5648fc1e191a3f869a575b799d2225" } } $('.js-work-strip[data-work-id=116584430]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116584430,"title":"Corrigendum: Similarity degree of Fourier algebras","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes the matricial open unit ball b 1 (M n ⊗ V 0) onto b 1 (M n ⊗ [V 0 /(V 0 ∩ W)]) ∼ = b 1 ([M n ⊗ V 0 ]/[M n ⊗ (V 0 ∩ W)]). We now recall the notation of [7]. For a Banach algebra and operator space A, c ≥ 1, A c (contained in B(H c)) is the universal operator algebra generated by representations on Hilbert spaces π : A → B(H) with completely bounded norm π cb ≤ c, and ι c : A → A c is the canonical embedding. Note that we assume that ι 1 is injective. We say that A satisfies the similarity property for completely bounded homomorphims if for each completely bounded homomorphim π : A → B(H), there is an invertible S in B(H) for which Sπ(•)S −1 cb ≤ 1. We also consider the \"weighted multiplication\" map on the N-fold Haagerup tensor product of A with itself, m N,c : A N ⊗ h → A c , given on elementary tensor by m N,c (u 1 ⊗ • • • ⊗ u N) = 1 c N ι c (u 1). .. ι c (u n) = 1 c N ι c (u 1 ,. .. u N) which is a complete contraction.","publication_date":{"day":null,"month":null,"year":2018,"errors":{}},"publication_name":"Journal of Functional Analysis","grobid_abstract_attachment_id":112673830},"translated_abstract":null,"internal_url":"https://www.academia.edu/116584430/Corrigendum_Similarity_degree_of_Fourier_algebras","translated_internal_url":"","created_at":"2024-03-23T02:37:55.040-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112673830,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673830/thumbnails/1.jpg","file_name":"1808.pdf","download_url":"https://www.academia.edu/attachments/112673830/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Corrigendum_Similarity_degree_of_Fourier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673830/1808-libre.pdf?1711188562=\u0026response-content-disposition=attachment%3B+filename%3DCorrigendum_Similarity_degree_of_Fourier.pdf\u0026Expires=1733907351\u0026Signature=LqcVTwfojhmFwyA9S4o0pEtfXlw9SKGfRFS2E0OFSEuwAGYAYgJ5fjIozcNO0nTYP93IKKQLbhc4QDMvmD17iNp1jtq06~pOcg7NK~FE~XZefQCOsqUMaElxu5yPy3iVwH8r9D29NdJw1fvMmzYuwdLEBoCSATFEg9p0PL9tqvOJHCZI81TPuyRJ6lrNhpgMul3rhNLnGvun8V8MTBk~WJM820C969Os3kGt9huowyXbS56e-5HyRSrrIkdxGbTXcxSvIdb-1V1KpiIprla078z95FtR0C8q~szSRe9Dbnm2PPsKs9c4Tdpw6dy1F9N89NU3Tg0Qtf3QJPzpVAl52A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Corrigendum_Similarity_degree_of_Fourier_algebras","translated_slug":"","page_count":6,"language":"en","content_type":"Work","summary":"Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes the matricial open unit ball b 1 (M n ⊗ V 0) onto b 1 (M n ⊗ [V 0 /(V 0 ∩ W)]) ∼ = b 1 ([M n ⊗ V 0 ]/[M n ⊗ (V 0 ∩ W)]). We now recall the notation of [7]. For a Banach algebra and operator space A, c ≥ 1, A c (contained in B(H c)) is the universal operator algebra generated by representations on Hilbert spaces π : A → B(H) with completely bounded norm π cb ≤ c, and ι c : A → A c is the canonical embedding. Note that we assume that ι 1 is injective. We say that A satisfies the similarity property for completely bounded homomorphims if for each completely bounded homomorphim π : A → B(H), there is an invertible S in B(H) for which Sπ(•)S −1 cb ≤ 1. We also consider the \"weighted multiplication\" map on the N-fold Haagerup tensor product of A with itself, m N,c : A N ⊗ h → A c , given on elementary tensor by m N,c (u 1 ⊗ • • • ⊗ u N) = 1 c N ι c (u 1). .. ι c (u n) = 1 c N ι c (u 1 ,. .. u N) which is a complete contraction.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":112673830,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673830/thumbnails/1.jpg","file_name":"1808.pdf","download_url":"https://www.academia.edu/attachments/112673830/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Corrigendum_Similarity_degree_of_Fourier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673830/1808-libre.pdf?1711188562=\u0026response-content-disposition=attachment%3B+filename%3DCorrigendum_Similarity_degree_of_Fourier.pdf\u0026Expires=1733907351\u0026Signature=LqcVTwfojhmFwyA9S4o0pEtfXlw9SKGfRFS2E0OFSEuwAGYAYgJ5fjIozcNO0nTYP93IKKQLbhc4QDMvmD17iNp1jtq06~pOcg7NK~FE~XZefQCOsqUMaElxu5yPy3iVwH8r9D29NdJw1fvMmzYuwdLEBoCSATFEg9p0PL9tqvOJHCZI81TPuyRJ6lrNhpgMul3rhNLnGvun8V8MTBk~WJM820C969Os3kGt9huowyXbS56e-5HyRSrrIkdxGbTXcxSvIdb-1V1KpiIprla078z95FtR0C8q~szSRe9Dbnm2PPsKs9c4Tdpw6dy1F9N89NU3Tg0Qtf3QJPzpVAl52A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":390056,"name":"Fourier transform","url":"https://www.academia.edu/Documents/in/Fourier_transform"},{"id":1713495,"name":"Degree in music","url":"https://www.academia.edu/Documents/in/Degree_in_music"},{"id":3847659,"name":"Similarity Geometry","url":"https://www.academia.edu/Documents/in/Similarity_Geometry"}],"urls":[{"id":40541366,"url":"https://api.elsevier.com/content/article/PII:S0022123618303914?httpAccept=text/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982388"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982388/Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity"><img alt="Research paper thumbnail of Beurling-Fourier algebras, operator amenability and Arens regularity" class="work-thumbnail" src="https://attachments.academia-assets.com/82302097/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982388/Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity">Beurling-Fourier algebras, operator amenability and Arens regularity</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5c488adb6f636d9c030302047b4779df" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302097,"asset_id":73982388,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302097/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982388"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982388"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982388; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982388]").text(description); $(".js-view-count[data-work-id=73982388]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982388; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982388']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982388, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "5c488adb6f636d9c030302047b4779df" } } $('.js-work-strip[data-work-id=73982388]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982388,"title":"Beurling-Fourier algebras, operator amenability and Arens regularity","translated_title":"","metadata":{"abstract":"We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).","publication_date":{"day":1,"month":9,"year":2010,"errors":{}}},"translated_abstract":"We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).","internal_url":"https://www.academia.edu/73982388/Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity","translated_internal_url":"","created_at":"2022-03-17T21:40:37.750-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302097,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302097/thumbnails/1.jpg","file_name":"1009.0094.pdf","download_url":"https://www.academia.edu/attachments/82302097/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Beurling_Fourier_algebras_operator_amena.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302097/1009.0094-libre.pdf?1647582028=\u0026response-content-disposition=attachment%3B+filename%3DBeurling_Fourier_algebras_operator_amena.pdf\u0026Expires=1733907351\u0026Signature=a~mMOQZhs02zua8J1q66Z5ViDuQJ3zCGw8ChRDoXraXWbAIooX8-9~IsOHBRYxv9mJaufrTEArU2znRycuiHaUnmSAvbLQnEWyYalQaa1GLpZoPaPeH4h3YIDGpFufcVLd6y1-vbrtHEcimyGPObYOncDFsvCs9lixUH-5wb-x7zD6nyvoMxeP-lbMQayGejE2erZ6kAzGm1WBNO0EOuV0NPgVwRJGZM-WBxdLXd3AW4JjBb2x-3etyw9wWHax9HSRl43RodgJC1vQp93ij71jmKuXhbdalSxRsO~lrHfSQg48jrj25~0umw9va4wz1GVjdb59JelUgpggfhCHhfaA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity","translated_slug":"","page_count":42,"language":"en","content_type":"Work","summary":"We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302097,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302097/thumbnails/1.jpg","file_name":"1009.0094.pdf","download_url":"https://www.academia.edu/attachments/82302097/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Beurling_Fourier_algebras_operator_amena.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302097/1009.0094-libre.pdf?1647582028=\u0026response-content-disposition=attachment%3B+filename%3DBeurling_Fourier_algebras_operator_amena.pdf\u0026Expires=1733907351\u0026Signature=a~mMOQZhs02zua8J1q66Z5ViDuQJ3zCGw8ChRDoXraXWbAIooX8-9~IsOHBRYxv9mJaufrTEArU2znRycuiHaUnmSAvbLQnEWyYalQaa1GLpZoPaPeH4h3YIDGpFufcVLd6y1-vbrtHEcimyGPObYOncDFsvCs9lixUH-5wb-x7zD6nyvoMxeP-lbMQayGejE2erZ6kAzGm1WBNO0EOuV0NPgVwRJGZM-WBxdLXd3AW4JjBb2x-3etyw9wWHax9HSRl43RodgJC1vQp93ij71jmKuXhbdalSxRsO~lrHfSQg48jrj25~0umw9va4wz1GVjdb59JelUgpggfhCHhfaA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302096,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302096/thumbnails/1.jpg","file_name":"1009.0094.pdf","download_url":"https://www.academia.edu/attachments/82302096/download_file","bulk_download_file_name":"Beurling_Fourier_algebras_operator_amena.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302096/1009.0094-libre.pdf?1647582028=\u0026response-content-disposition=attachment%3B+filename%3DBeurling_Fourier_algebras_operator_amena.pdf\u0026Expires=1733907351\u0026Signature=dPSK62FoKcD6z9-UmULfgDXRJcNwXUWkY5fyYFd7kWCLkG7~pl90Dix85NDr-ebUElxffGWfsZqZnNY4FRbNqSlacUcWoaAq2fJb9TYGWM3zKh1kZ4ydXmV-pgUiGzAYgkc~ntGmb1ib16L~Vlwkl~XIOnOgzf87mpjmS~F0N1Ux9BzNc6wJIfKFvSbUk0qI6i-MGP6ejNt4JWVbYS4MSgzTxVbxnnSl1d3oyy3N7e56~Dpe-~aCTsC5xjgPzf2tq0rKXM-IxPgqJK6S9oafSgdT~qAgcJsdSLH6VH3iLFtx2wwAr0p78PUbzoRf91RYRL-MC6ivclnGaA1dQOfYaw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":2756578,"name":"Unitary group","url":"https://www.academia.edu/Documents/in/Unitary_group"}],"urls":[{"id":18589301,"url":"https://archive.org/download/arxiv-1009.0094/1009.0094.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982387"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982387/Similarity_degree_of_Fourier_algebras"><img alt="Research paper thumbnail of Similarity degree of Fourier algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/82302100/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982387/Similarity_degree_of_Fourier_algebras">Similarity degree of Fourier algebras</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that for a locally compact group G, amongst a class which contains amenable and small inv...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier&#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6d62dd583568f2389e9ea569ac67827b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302100,"asset_id":73982387,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302100/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982387"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982387"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982387; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982387]").text(description); $(".js-view-count[data-work-id=73982387]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982387; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982387']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982387, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6d62dd583568f2389e9ea569ac67827b" } } $('.js-work-strip[data-work-id=73982387]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982387,"title":"Similarity degree of Fourier algebras","translated_title":"","metadata":{"abstract":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier\u0026#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.","publication_date":{"day":18,"month":3,"year":2016,"errors":{}}},"translated_abstract":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier\u0026#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.","internal_url":"https://www.academia.edu/73982387/Similarity_degree_of_Fourier_algebras","translated_internal_url":"","created_at":"2022-03-17T21:40:37.557-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302100,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302100/thumbnails/1.jpg","file_name":"1511.03423v3.pdf","download_url":"https://www.academia.edu/attachments/82302100/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Similarity_degree_of_Fourier_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302100/1511.03423v3-libre.pdf?1647582022=\u0026response-content-disposition=attachment%3B+filename%3DSimilarity_degree_of_Fourier_algebras.pdf\u0026Expires=1733907351\u0026Signature=TBLRxoYpZd2OT5dWIV~DEMhlV5lQygJp9zdxLwnEwqkaQzT6-DIjhp8xQ5BWTb5CiLHNz-zzdNpb6AtPjui7sSPHBZNWaQsFOlLv2Jo6pIZwg565lR9PXy0ThDfrPDP2h6gNuLIq1RXak3VMD16SNr5uS7hY~XlvkAWE6U8FOeITXtSzom-xdgJD46NoN77XuZCBrRwGV7nJ8EZVs7eszrhdZfrElb7BVxDBSF5rQVHQpKKLEUZecu3p9BoB9~9pS2h0r7nECpPU-2xm5NuqS6WraBmhAEGYQUIrvPS45P5fx2orI7ySwTSYrKjfNrEOadP0F09RoJhPRdMRL5iB1A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Similarity_degree_of_Fourier_algebras","translated_slug":"","page_count":14,"language":"en","content_type":"Work","summary":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier\u0026#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302100,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302100/thumbnails/1.jpg","file_name":"1511.03423v3.pdf","download_url":"https://www.academia.edu/attachments/82302100/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Similarity_degree_of_Fourier_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302100/1511.03423v3-libre.pdf?1647582022=\u0026response-content-disposition=attachment%3B+filename%3DSimilarity_degree_of_Fourier_algebras.pdf\u0026Expires=1733907351\u0026Signature=TBLRxoYpZd2OT5dWIV~DEMhlV5lQygJp9zdxLwnEwqkaQzT6-DIjhp8xQ5BWTb5CiLHNz-zzdNpb6AtPjui7sSPHBZNWaQsFOlLv2Jo6pIZwg565lR9PXy0ThDfrPDP2h6gNuLIq1RXak3VMD16SNr5uS7hY~XlvkAWE6U8FOeITXtSzom-xdgJD46NoN77XuZCBrRwGV7nJ8EZVs7eszrhdZfrElb7BVxDBSF5rQVHQpKKLEUZecu3p9BoB9~9pS2h0r7nECpPU-2xm5NuqS6WraBmhAEGYQUIrvPS45P5fx2orI7ySwTSYrKjfNrEOadP0F09RoJhPRdMRL5iB1A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589300,"url":"https://arxiv.org/pdf/1511.03423v3.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982386"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982386/Distance_k_graphs_of_hypercube_and_q_Hermite_polynomials"><img alt="Research paper thumbnail of Distance k-graphs of hypercube and q-Hermite polynomials" class="work-thumbnail" src="https://attachments.academia-assets.com/82302095/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982386/Distance_k_graphs_of_hypercube_and_q_Hermite_polynomials">Distance k-graphs of hypercube and q-Hermite polynomials</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We will prove that some weighted graphs on the distance k-graph of hypercubes approximate the q-H...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We will prove that some weighted graphs on the distance k-graph of hypercubes approximate the q-Hermite polynomial of a q-gaussian variable by providing an appropriate matrix model.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9f33433b4e75c6b1050c226001e70c6c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302095,"asset_id":73982386,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302095/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982386"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982386"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982386; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982385"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982385/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups"><img alt="Research paper thumbnail of New deformations of Convolution algebras and Fourier algebras on locally compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/82302094/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982385/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups">New deformations of Convolution algebras and Fourier algebras on locally compact groups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on lo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4d6a0e0da51340c1203877ada2ae2ec7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302094,"asset_id":73982385,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302094/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982385"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982385"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982385; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982385]").text(description); $(".js-view-count[data-work-id=73982385]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982385; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982385']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982385, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4d6a0e0da51340c1203877ada2ae2ec7" } } $('.js-work-strip[data-work-id=73982385]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982385,"title":"New deformations of Convolution algebras and Fourier algebras on locally compact groups","translated_title":"","metadata":{"abstract":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.","publication_date":{"day":5,"month":8,"year":2015,"errors":{}}},"translated_abstract":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.","internal_url":"https://www.academia.edu/73982385/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups","translated_internal_url":"","created_at":"2022-03-17T21:40:37.184-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302094,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302094/thumbnails/1.jpg","file_name":"1508.01092v1.pdf","download_url":"https://www.academia.edu/attachments/82302094/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"New_deformations_of_Convolution_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302094/1508.01092v1-libre.pdf?1647582023=\u0026response-content-disposition=attachment%3B+filename%3DNew_deformations_of_Convolution_algebras.pdf\u0026Expires=1733907351\u0026Signature=Bred7TZfZV7ybjXNHD1YtEFekAQeapUrneWwoHTs5B00YvQkSqfXSMCrqSV-P3sSb8amwfAbTmlD37F48PA40YsEARxNb-vJgO5~lxSvZiVM97VSepkSYx9dqhePAhijyZxCrPxSjhj3z2~oXtlJk6sYWX6--EeRbxBrVqzYZZS7uYsyWo9VrTA8qFefxyOaKYVTUZ-4dlvNpOYDioG0ujmtI0xEV1HC~FGOiUcPKSIFZjUfof0L-mR1J2vG19NfyzzE1c3SnCrZqZwd0uwkGRIQe7tDvj9A1IcGsVZo9I~CzJaJU~9-07zem8-JKjXFq3TkfPBWaEEB5Kjesf~rRQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups","translated_slug":"","page_count":17,"language":"en","content_type":"Work","summary":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. 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For a fixed k&gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d081ded98cd423f67190286fbf29ab41" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302093,"asset_id":73982384,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302093/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982384"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982384"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982384; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982384]").text(description); $(".js-view-count[data-work-id=73982384]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982384; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982384']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982384, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d081ded98cd423f67190286fbf29ab41" } } $('.js-work-strip[data-work-id=73982384]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982384,"title":"Asymptotic Spectral Distributions of Distance k-Graphs of Cartesian Product Graphs","translated_title":"","metadata":{"abstract":"Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k\u0026gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","publication_date":{"day":8,"month":4,"year":2013,"errors":{}}},"translated_abstract":"Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k\u0026gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","internal_url":"https://www.academia.edu/73982384/Asymptotic_Spectral_Distributions_of_Distance_k_Graphs_of_Cartesian_Product_Graphs","translated_internal_url":"","created_at":"2022-03-17T21:40:36.998-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302093,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302093/thumbnails/1.jpg","file_name":"1304.1236.pdf","download_url":"https://www.academia.edu/attachments/82302093/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotic_Spectral_Distributions_of_Dis.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302093/1304.1236-libre.pdf?1647582023=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotic_Spectral_Distributions_of_Dis.pdf\u0026Expires=1733907351\u0026Signature=QOvFgdYPdXuRJvAP4OL4xyHgdplIk11qJ3ubPBE5n~~iwq6NqkeHdGGXGdBXpZf4A08gENacUXV1PI2w6Vuwl8iRttdlNT3rub7ZXv91-1HKXDm0LaiBL1vUlY2a~gD11PyzR9I31uxjeDoh0yY0dLTcH3GiXTtnN-4~x3gvnI8R0uWzRPc0rSBPTWo3N6RRaQi09wzvjBXzbfrZoPCEoFksq7LPYWwZkUcPn9gpzYi4FF3lSwOB5i80nNnX2qKHRhFNFu7dUW7TCdqGRmiilT~lCtosDzznWyprQ3yOznglLoGCBBC91sCRL3cK76GGwiQS2fPDhzZf1C~AZ2WcbQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Asymptotic_Spectral_Distributions_of_Distance_k_Graphs_of_Cartesian_Product_Graphs","translated_slug":"","page_count":13,"language":"en","content_type":"Work","summary":"Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k\u0026gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302093,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302093/thumbnails/1.jpg","file_name":"1304.1236.pdf","download_url":"https://www.academia.edu/attachments/82302093/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotic_Spectral_Distributions_of_Dis.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302093/1304.1236-libre.pdf?1647582023=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotic_Spectral_Distributions_of_Dis.pdf\u0026Expires=1733907351\u0026Signature=QOvFgdYPdXuRJvAP4OL4xyHgdplIk11qJ3ubPBE5n~~iwq6NqkeHdGGXGdBXpZf4A08gENacUXV1PI2w6Vuwl8iRttdlNT3rub7ZXv91-1HKXDm0LaiBL1vUlY2a~gD11PyzR9I31uxjeDoh0yY0dLTcH3GiXTtnN-4~x3gvnI8R0uWzRPc0rSBPTWo3N6RRaQi09wzvjBXzbfrZoPCEoFksq7LPYWwZkUcPn9gpzYi4FF3lSwOB5i80nNnX2qKHRhFNFu7dUW7TCdqGRmiilT~lCtosDzznWyprQ3yOznglLoGCBBC91sCRL3cK76GGwiQS2fPDhzZf1C~AZ2WcbQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589297,"url":"https://archive.org/download/arxiv-1304.1236/1304.1236.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982382"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982382/p_Fourier_algebras_on_compact_groups"><img alt="Research paper thumbnail of p-Fourier algebras on compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/82302099/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982382/p_Fourier_algebras_on_compact_groups">p-Fourier algebras on compact groups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p&gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="228fd10866ad5e7b8cbc852b69b05e72" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302099,"asset_id":73982382,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302099/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982382"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982382"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982382; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982382]").text(description); $(".js-view-count[data-work-id=73982382]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982382; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982382']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982382, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "228fd10866ad5e7b8cbc852b69b05e72" } } $('.js-work-strip[data-work-id=73982382]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982382,"title":"p-Fourier algebras on compact groups","translated_title":"","metadata":{"abstract":"Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p\u0026gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.","publication_date":{"day":17,"month":2,"year":2015,"errors":{}}},"translated_abstract":"Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p\u0026gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.","internal_url":"https://www.academia.edu/73982382/p_Fourier_algebras_on_compact_groups","translated_internal_url":"","created_at":"2022-03-17T21:40:36.812-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302099/thumbnails/1.jpg","file_name":"1411.2336v2.pdf","download_url":"https://www.academia.edu/attachments/82302099/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"p_Fourier_algebras_on_compact_groups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302099/1411.2336v2-libre.pdf?1647582030=\u0026response-content-disposition=attachment%3B+filename%3Dp_Fourier_algebras_on_compact_groups.pdf\u0026Expires=1733907351\u0026Signature=Bj2vKT3H0UdNkA4XTGAac-EPikngssb7N3Ata0LGCKDBW7h99fO3SWb5HXJE1dDyIfYM6~tWqlSm2L8H0XkZgWOnRsgUSFLcymH1h8QksiMhkZZtV6vczknx5DQmOuc3tzG5SfEonovGCFY6E1Az8B8SKwnfBtJ7~sMtMnfBycoaSGtZkzo0ZBdl7CedpBpeOR0~9LAT8iNxGj8lMlZvLWHEw-wzeXmueJeeejYggg~XToep5llXhaJ2uv67PJZsz~2Kwm6vMc0MuaufkA61up-Mp1lmFaWtUEuTIg8VOtpaIYMvpa2qPIH8etJlLDMJWr6LZBPEGwjQrgpxG9oC7g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"p_Fourier_algebras_on_compact_groups","translated_slug":"","page_count":41,"language":"en","content_type":"Work","summary":"Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p\u0026gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302099/thumbnails/1.jpg","file_name":"1411.2336v2.pdf","download_url":"https://www.academia.edu/attachments/82302099/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"p_Fourier_algebras_on_compact_groups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302099/1411.2336v2-libre.pdf?1647582030=\u0026response-content-disposition=attachment%3B+filename%3Dp_Fourier_algebras_on_compact_groups.pdf\u0026Expires=1733907351\u0026Signature=Bj2vKT3H0UdNkA4XTGAac-EPikngssb7N3Ata0LGCKDBW7h99fO3SWb5HXJE1dDyIfYM6~tWqlSm2L8H0XkZgWOnRsgUSFLcymH1h8QksiMhkZZtV6vczknx5DQmOuc3tzG5SfEonovGCFY6E1Az8B8SKwnfBtJ7~sMtMnfBycoaSGtZkzo0ZBdl7CedpBpeOR0~9LAT8iNxGj8lMlZvLWHEw-wzeXmueJeeejYggg~XToep5llXhaJ2uv67PJZsz~2Kwm6vMc0MuaufkA61up-Mp1lmFaWtUEuTIg8VOtpaIYMvpa2qPIH8etJlLDMJWr6LZBPEGwjQrgpxG9oC7g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302098,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302098/thumbnails/1.jpg","file_name":"1411.2336v2.pdf","download_url":"https://www.academia.edu/attachments/82302098/download_file","bulk_download_file_name":"p_Fourier_algebras_on_compact_groups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302098/1411.2336v2-libre.pdf?1647582030=\u0026response-content-disposition=attachment%3B+filename%3Dp_Fourier_algebras_on_compact_groups.pdf\u0026Expires=1733907351\u0026Signature=DhSA~S0h0E3bH6tLrYPjinKbbojM3fJ0R64L6XE~i1geR8jnUqrn7b9NM7-i65VpDjsSnbrNah12YudltXveE0KfyxiGu2omrZr0j-O5YX8s8ZfhXhwmDQkcX1u-EWXwuPAB7AgY24aUQNQKApx6v0zFBPjPNuF7D56JykP2XXta7qQrVUz6SPCOtX9NwdKK6yBK6KgyZVyYnZ2nszbcb8ItkEQL-6ez~bpB1349n6MHFtj7m8OGyGmnlreVYwyQDN5FAZnn4cPg2KPb5jinL1zCawQlP5GzJEFBgvfNBsfPsZ6li2h2Zy0o7~8uhuCovEbi1fBFhS94CL7mLe0Arw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589295,"url":"https://arxiv.org/pdf/1411.2336v2.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982380"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982380/Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras"><img alt="Research paper thumbnail of Integration over the quantum diagonal subgroup and associated Fourier-like algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/82302087/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982380/Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras">Integration over the quantum diagonal subgroup and associated Fourier-like algebras</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N&gt; 2, associated to Wang&#39;s free orthogonal groups, and show that they are not operator weakly amenable.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d46de7c3b05b20a66d24a78c5f3b999b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302087,"asset_id":73982380,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302087/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982380"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982380"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982380; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982380]").text(description); $(".js-view-count[data-work-id=73982380]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982380; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982380']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982380, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d46de7c3b05b20a66d24a78c5f3b999b" } } $('.js-work-strip[data-work-id=73982380]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982380,"title":"Integration over the quantum diagonal subgroup and associated Fourier-like algebras","translated_title":"","metadata":{"abstract":"By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N\u0026gt; 2, associated to Wang\u0026#39;s free orthogonal groups, and show that they are not operator weakly amenable.","publication_date":{"day":15,"month":6,"year":2016,"errors":{}}},"translated_abstract":"By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N\u0026gt; 2, associated to Wang\u0026#39;s free orthogonal groups, and show that they are not operator weakly amenable.","internal_url":"https://www.academia.edu/73982380/Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras","translated_internal_url":"","created_at":"2022-03-17T21:40:36.627-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302087,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302087/thumbnails/1.jpg","file_name":"1605.02705v2.pdf","download_url":"https://www.academia.edu/attachments/82302087/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Integration_over_the_quantum_diagonal_su.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302087/1605.02705v2-libre.pdf?1647582027=\u0026response-content-disposition=attachment%3B+filename%3DIntegration_over_the_quantum_diagonal_su.pdf\u0026Expires=1733907351\u0026Signature=C7v2TOmyXFJJYCCaHJrBWbZcsv72Ctx7TjjYdJvA2Sq9MVBIJdNeOBvGrrXM8K5kaYsvBGwXcNnnqDD9uM0XbbrLepjIgv~2z~Hf8MKOClhvzE5Bh3VmWqJc8BfW16dOlUgRK3401zR0HKivF5aiRqoYfmpVahas~Xsl3SnyLCVFx~I5Tw06~fB3lOBCp6q3I2Nao8TOg3I6e0ow-yhduxd~V~JPtJUY6-BzlZwSW1AApCUJUq9y2jQyGpAeRVK97PZeQYagR60HlrLVWZuKXez0uK3j6Kca09saPFGh9eiqvOOkgV2AWPNl4meRG7U-dQD81FI~ydIiLMJhAugBUA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras","translated_slug":"","page_count":31,"language":"en","content_type":"Work","summary":"By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N\u0026gt; 2, associated to Wang\u0026#39;s free orthogonal groups, and show that they are not operator weakly amenable.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302087,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302087/thumbnails/1.jpg","file_name":"1605.02705v2.pdf","download_url":"https://www.academia.edu/attachments/82302087/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Integration_over_the_quantum_diagonal_su.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302087/1605.02705v2-libre.pdf?1647582027=\u0026response-content-disposition=attachment%3B+filename%3DIntegration_over_the_quantum_diagonal_su.pdf\u0026Expires=1733907351\u0026Signature=C7v2TOmyXFJJYCCaHJrBWbZcsv72Ctx7TjjYdJvA2Sq9MVBIJdNeOBvGrrXM8K5kaYsvBGwXcNnnqDD9uM0XbbrLepjIgv~2z~Hf8MKOClhvzE5Bh3VmWqJc8BfW16dOlUgRK3401zR0HKivF5aiRqoYfmpVahas~Xsl3SnyLCVFx~I5Tw06~fB3lOBCp6q3I2Nao8TOg3I6e0ow-yhduxd~V~JPtJUY6-BzlZwSW1AApCUJUq9y2jQyGpAeRVK97PZeQYagR60HlrLVWZuKXez0uK3j6Kca09saPFGh9eiqvOOkgV2AWPNl4meRG7U-dQD81FI~ydIiLMJhAugBUA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302088,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302088/thumbnails/1.jpg","file_name":"1605.02705v2.pdf","download_url":"https://www.academia.edu/attachments/82302088/download_file","bulk_download_file_name":"Integration_over_the_quantum_diagonal_su.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302088/1605.02705v2-libre.pdf?1647582026=\u0026response-content-disposition=attachment%3B+filename%3DIntegration_over_the_quantum_diagonal_su.pdf\u0026Expires=1733907351\u0026Signature=XbWtuE~fnK38mzeMV1iUhD2HE0S8rbMrtMavcC~NetsXDs3-Wcvs9vWtiW7VopRKeyU7K-h5FNSKZ44vrDQTOFMThxJYaRoZK0VJVuMS~2xRAZy3Oaew8PyWtoUl16R57so5EOI3TySpOPmu2ai15UTAkjhox6GnUE8M4QE7IR3GWrs8OnMVDRhKCBHzOApZuLFzIU737gMIoooQ9FeNClB4dy7eZxoDsO0rxn775EwlpB~apNJbQCsfPBtj8ypKKtuvRLmnzFx9dyPtlPDo0wSz0PkRxmPL-pBjpkhd9g~HummzBEuLgxLqTf8ht-IkA9~0HC0Bv3JJWEXulz260Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589293,"url":"https://arxiv.org/pdf/1605.02705v2.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982378"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal"><img alt="Research paper thumbnail of Weak amenability of Fourier algebras and local synthesis of the anti-diagonal" class="work-thumbnail" src="https://attachments.academia-assets.com/82302086/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal">Weak amenability of Fourier algebras and local synthesis of the anti-diagonal</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="58652a07ef7087b385d38a1fa9a10a0b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302086,"asset_id":73982378,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302086/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982378"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982378"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982378; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982378]").text(description); $(".js-view-count[data-work-id=73982378]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982378; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982378']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982378, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "58652a07ef7087b385d38a1fa9a10a0b" } } $('.js-work-strip[data-work-id=73982378]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982378,"title":"Weak amenability of Fourier algebras and local synthesis of the anti-diagonal","translated_title":"","metadata":{"abstract":"We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.","publication_date":{"day":18,"month":2,"year":2015,"errors":{}}},"translated_abstract":"We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.","internal_url":"https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal","translated_internal_url":"","created_at":"2022-03-17T21:40:36.446-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302086,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302086/thumbnails/1.jpg","file_name":"1502.05214v1.pdf","download_url":"https://www.academia.edu/attachments/82302086/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Weak_amenability_of_Fourier_algebras_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302086/1502.05214v1-libre.pdf?1647582025=\u0026response-content-disposition=attachment%3B+filename%3DWeak_amenability_of_Fourier_algebras_and.pdf\u0026Expires=1733907351\u0026Signature=L1L5vV-L-u~zRl3voyv3Qlgf9L5tbj18LdZwMOaQok835zGHzKcoWRqk4QnLc0bWmW~8saREWouRJHmLtj5GNvNM2GQmg8j46GZ0VZqI-nLbABMpWs7FWE17-BenmOM-uCVVG8vDvbtq1sLAMlAddESJ0IKt9OPxiMa3GPsBuaHvQ26dgpwpq-VW~membj8DdBaUw4IYLpOc7jzl0DxTmYJs3sFxvmrPa8omCo-MFwyBNRFJ-GFP9gz1ptqgIXqxqoiGUnzcxr0epiGnluqP9KYiAh4~p51NXxH59Dj1uDCCQI0AUUt27C4UFXO7731pn994VQ5XSO7FB6riDO3oKA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal","translated_slug":"","page_count":24,"language":"en","content_type":"Work","summary":"We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302086,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302086/thumbnails/1.jpg","file_name":"1502.05214v1.pdf","download_url":"https://www.academia.edu/attachments/82302086/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Weak_amenability_of_Fourier_algebras_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302086/1502.05214v1-libre.pdf?1647582025=\u0026response-content-disposition=attachment%3B+filename%3DWeak_amenability_of_Fourier_algebras_and.pdf\u0026Expires=1733907351\u0026Signature=L1L5vV-L-u~zRl3voyv3Qlgf9L5tbj18LdZwMOaQok835zGHzKcoWRqk4QnLc0bWmW~8saREWouRJHmLtj5GNvNM2GQmg8j46GZ0VZqI-nLbABMpWs7FWE17-BenmOM-uCVVG8vDvbtq1sLAMlAddESJ0IKt9OPxiMa3GPsBuaHvQ26dgpwpq-VW~membj8DdBaUw4IYLpOc7jzl0DxTmYJs3sFxvmrPa8omCo-MFwyBNRFJ-GFP9gz1ptqgIXqxqoiGUnzcxr0epiGnluqP9KYiAh4~p51NXxH59Dj1uDCCQI0AUUt27C4UFXO7731pn994VQ5XSO7FB6riDO3oKA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302085,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302085/thumbnails/1.jpg","file_name":"1502.05214v1.pdf","download_url":"https://www.academia.edu/attachments/82302085/download_file","bulk_download_file_name":"Weak_amenability_of_Fourier_algebras_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302085/1502.05214v1-libre.pdf?1647582024=\u0026response-content-disposition=attachment%3B+filename%3DWeak_amenability_of_Fourier_algebras_and.pdf\u0026Expires=1733907351\u0026Signature=XHS5EhlV6pK6Ot9xvwb8qApNE07TgX1gGuqmjd9uzJ9WEz-RBxLMhZcxXBRLibiUZNhEeJzLdihXKWqwXbuDJLq4eN-FNqmUtnWJuAmVDA5GiUR2dXJuvUhWo3jns917YPKmMi4pMKys9r0xasNmLt9TLdxgg0AHihG5FfFWOzkK5D4SwoZV0uZcuP2ja~ULLZmAOzYz5HpcrXjHWoqu~nkXrHKR3Gfqfdy2Q2Z1NAe3xeUYJULHhf27CBBkJC2BJaJyMblB4cSuB2SpR0ND7bzsj66OJ9K6PqXPflDEE80cmVLfJPGrUWG67DR2v9ErON0YU6xwT3WPE8TincSNwg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589291,"url":"https://arxiv.org/pdf/1502.05214v1.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982375"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982375/Quantum_channels_with_quantum_group_symmetry"><img alt="Research paper thumbnail of Quantum channels with quantum group symmetry" class="work-thumbnail" src="https://attachments.academia-assets.com/82302083/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982375/Quantum_channels_with_quantum_group_symmetry">Quantum channels with quantum group symmetry</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups f...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion rule, which provides a wide generalization of some recent results. The presence of quantum group symmetry contrast to the group symmetry will be highlighted in the examples of quantum permutation groups and SU_q(2). In the latter example, we will see the necessity of the Heisenberg picture coming from the non-Kac type condition. This paper ends with the covariance with respect to projective representations, which leads us back to Weyl covariant channels and its fermionic analogue.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="08b40bd78c03b3e7ddb0be513a424610" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302083,"asset_id":73982375,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302083/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982375"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982375"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982375; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982375]").text(description); $(".js-view-count[data-work-id=73982375]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982375; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982375']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982375, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "08b40bd78c03b3e7ddb0be513a424610" } } $('.js-work-strip[data-work-id=73982375]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982375,"title":"Quantum channels with quantum group symmetry","translated_title":"","metadata":{"abstract":"In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion rule, which provides a wide generalization of some recent results. The presence of quantum group symmetry contrast to the group symmetry will be highlighted in the examples of quantum permutation groups and SU_q(2). In the latter example, we will see the necessity of the Heisenberg picture coming from the non-Kac type condition. This paper ends with the covariance with respect to projective representations, which leads us back to Weyl covariant channels and its fermionic analogue.","publication_date":{"day":8,"month":7,"year":2020,"errors":{}}},"translated_abstract":"In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982371"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982371/Quantum_Channels_with_Quantum_Group_Symmetry"><img alt="Research paper thumbnail of Quantum Channels with Quantum Group Symmetry" class="work-thumbnail" src="https://attachments.academia-assets.com/82302160/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982371/Quantum_Channels_with_Quantum_Group_Symmetry">Quantum Channels with Quantum Group Symmetry</a></div><div class="wp-workCard_item"><span>Communications in Mathematical Physics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups f...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion rule, which provides a wide generalization of the results of [MSD17]. The presence of quantum group symmetry contrast to the group symmetry will be highlighted in the examples of quantum permutation groups and SU q (2). In the latter example, we will see the necessity of the Heisenberg picture coming from the non-Kac type condition. This paper ends with the covariance with respect to projective representations, which leads us back to Weyl covariant channels and its fermionic analogue.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6383898acbfe280c5470ed24aa4d9003" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302160,"asset_id":73982371,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302160/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982371"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982371"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982371; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982371]").text(description); $(".js-view-count[data-work-id=73982371]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982371; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982371']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982371, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6383898acbfe280c5470ed24aa4d9003" } } $('.js-work-strip[data-work-id=73982371]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982371,"title":"Quantum Channels with Quantum Group Symmetry","translated_title":"","metadata":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. 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Two-dimensional restricted lattices admitting the Kronecker product structure are listed, and their spectral distributions are calculated in terms of elliptic integrals.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="211040cb6e7330b77b7132811595a6c6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302079,"asset_id":73982369,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302079/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982369"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982369"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982369; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982369]").text(description); $(".js-view-count[data-work-id=73982369]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982369; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982369']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982369, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "211040cb6e7330b77b7132811595a6c6" } } $('.js-work-strip[data-work-id=73982369]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982369,"title":"Kronecker Product Graphs and Counting Walks in Restricted Lattices","translated_title":"","metadata":{"abstract":"Formulas are derived for counting walks in the Kronecker product of graphs, and the associated spectral distributions are obtained by the Mellin convolution of probability distributions. 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Two-dimensional restricted lattices admitting the Kronecker product structure are listed, and their spectral distributions are calculated in terms of elliptic integrals.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302079,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302079/thumbnails/1.jpg","file_name":"1607.06808v1.pdf","download_url":"https://www.academia.edu/attachments/82302079/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Kronecker_Product_Graphs_and_Counting_Wa.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302079/1607.06808v1-libre.pdf?1647582025=\u0026response-content-disposition=attachment%3B+filename%3DKronecker_Product_Graphs_and_Counting_Wa.pdf\u0026Expires=1733907351\u0026Signature=WEkVl1LlkiR3enJr4XeinKxKBPKRk2Rg79kuTndJU7u0R0jqC-8FHP4psQPqN0cOFLcP7AYfm41vAplzoPrayzWinb~gEUSNZQfl9ux9p4EFDsnteIycIbiDLfoZquf5p7JQwHuv5FH9-fflqBSlrQc12RZsrTv5nsw8ftZl2ix7WnZBNr5M2TJlMXRQc-nNtg3EKh60fQztgpUXrQtSC9~Pb~625fOOMe41tBhMg5DU1h1a3pNTa3HVB5gDa06-EOb7WNqnjxfGfwQNpK6Pl6~h6~nX4fb0hO2VqbFoarCJWjcckIlXdJ0dMpP0RVXiOEgGuz5inQXD60xs71dE-w__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302080,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302080/thumbnails/1.jpg","file_name":"1607.06808v1.pdf","download_url":"https://www.academia.edu/attachments/82302080/download_file","bulk_download_file_name":"Kronecker_Product_Graphs_and_Counting_Wa.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302080/1607.06808v1-libre.pdf?1647582024=\u0026response-content-disposition=attachment%3B+filename%3DKronecker_Product_Graphs_and_Counting_Wa.pdf\u0026Expires=1733907351\u0026Signature=YMOAyS-If6~aQBEerwU2MKIjOQzX6OjWxwNSxdQXCdQ2K2bIJOlu3uOGV1GuTRY26OJnrb9bwBRCkP01Y3tDtr1~BXw50hvlxusHBcrutG~pqWbQ-2gC9um8ES4cyu7x4C6d4EwIz9yBLfKT5yfIgOJ9uPFqwpVsrUSfwzoIkw9b1Q5eayuvj3e-UnNVQqV1~UPJGwWYJQ6vGyHgszER2WzoxEZh57lPaxAMsmzPozDEV1jDKrUgHy7z5bhxnmQOhBxZ962beLYrKe9pkTHKbv28Xb9Rcj8gIT7yr-ISM67cLZnX98pogbSFKjuVcWTnBEBYFqimcN-3kZsyG5kLQA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"}],"urls":[{"id":18589285,"url":"https://arxiv.org/pdf/1607.06808v1.pdf"}]}, dispatcherData: dispatcherData }); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982367"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982367/Similarity_degree_of_Fourier_algebras"><img alt="Research paper thumbnail of Similarity degree of Fourier algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/82302159/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982367/Similarity_degree_of_Fourier_algebras">Similarity degree of Fourier algebras</a></div><div class="wp-workCard_item"><span>Journal of Functional Analysis</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that for a locally compact group G, amongst a class which contains amenable and small inv...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier's similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π : A(G) → B(H) admits an invertible S in B(H) for which S S −1 ≤ π 2 cb and S −1 π(•)S extends to a *-representation of the C*-algebra C 0 (G). This significantly improves some results due to Brannan and Samei (</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4d8315dd894ef360405b860daca29355" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302159,"asset_id":73982367,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302159/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982367"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982367"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982367; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982367]").text(description); $(".js-view-count[data-work-id=73982367]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982367; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982367']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982367, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4d8315dd894ef360405b860daca29355" } } $('.js-work-strip[data-work-id=73982367]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982367,"title":"Similarity degree of Fourier algebras","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier's similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π : A(G) → B(H) admits an invertible S in B(H) for which S S −1 ≤ π 2 cb and S −1 π(•)S extends to a *-representation of the C*-algebra C 0 (G). 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Specifically, any completely bounded homomorphism π : A(G) → B(H) admits an invertible S in B(H) for which S S −1 ≤ π 2 cb and S −1 π(•)S extends to a *-representation of the C*-algebra C 0 (G). This significantly improves some results due to Brannan and Samei (","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302159,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302159/thumbnails/1.jpg","file_name":"1511.pdf","download_url":"https://www.academia.edu/attachments/82302159/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Similarity_degree_of_Fourier_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302159/1511-libre.pdf?1647582018=\u0026response-content-disposition=attachment%3B+filename%3DSimilarity_degree_of_Fourier_algebras.pdf\u0026Expires=1733907351\u0026Signature=PCMs2b8w4X~CTpg84xSaLBCGSF2EhGeaiyFggPA7GLHuWp3T2hkMwde2mQ0UD5BG6L-1UmupKyVYmQsgYHamFtPPaaWPJwKgwkwWoIWkEexjpI7foc2daIlB5MAViewyhhulpD4JQ1WCMvwO7f2OU~B-n64Di9sezTth9gRcdIGSbeemzTG4JwDM3g-PdGjsb8bMJniA8X14w1hKaCvl9Cfmciap4u3uRVGATmAiqAD2z3F1DT1S1kIlSj95y6tp~rhKUQSMayK6tZnOl4e81gL1aSDV-89~pvvpAcEVgfh1zZZA2SEy8aIxb3UnEeMDZk5Q6W83co0V-yL2u-YXCQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982366"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982366/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups"><img alt="Research paper thumbnail of New deformations of Convolution algebras and Fourier algebras on locally compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/83819308/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982366/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups">New deformations of Convolution algebras and Fourier algebras on locally compact groups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on lo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e1e5f96c180798695024b55339fd927c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83819308,"asset_id":73982366,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83819308/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982366"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982366"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982366; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982366]").text(description); $(".js-view-count[data-work-id=73982366]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982366; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982366']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982366, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e1e5f96c180798695024b55339fd927c" } } $('.js-work-strip[data-work-id=73982366]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982366,"title":"New deformations of Convolution algebras and Fourier algebras on locally compact groups","translated_title":"","metadata":{"grobid_abstract":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. 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We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 &lt;α&lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="274bcf7d6803c303accdf4b46b771077" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83819313,"asset_id":73982365,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83819313/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982365"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982365"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982365; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982365]").text(description); $(".js-view-count[data-work-id=73982365]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982365; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982365']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982365, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "274bcf7d6803c303accdf4b46b771077" } } $('.js-work-strip[data-work-id=73982365]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982365,"title":"Some Weighted Group Algebras are Operator Algebras","translated_title":"","metadata":{"abstract":"LetGbe a finitely generated group with polynomial growth, and letωbe a weight, i.e. a sub-multiplicative function onGwith positive values. We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 \u0026lt;α\u0026lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.","publisher":"Cambridge University Press (CUP)","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Proceedings of the Edinburgh Mathematical Society"},"translated_abstract":"LetGbe a finitely generated group with polynomial growth, and letωbe a weight, i.e. a sub-multiplicative function onGwith positive values. We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 \u0026lt;α\u0026lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.","internal_url":"https://www.academia.edu/73982365/Some_Weighted_Group_Algebras_are_Operator_Algebras","translated_internal_url":"","created_at":"2022-03-17T21:40:35.008-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":83819313,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/83819313/thumbnails/1.jpg","file_name":"Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf","download_url":"https://www.academia.edu/attachments/83819313/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Weighted_Group_Algebras_are_Operato.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/83819313/Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf?1649706689=\u0026response-content-disposition=attachment%3B+filename%3DSome_Weighted_Group_Algebras_are_Operato.pdf\u0026Expires=1733907351\u0026Signature=ExKXoQuKMgJ3q3YBGEEsStXr3UbhAySxvb9pIAPsxi7rtTqDPx2ejiYLEzRHLsrYYpk2DwSOLG94Xm8Lrl~B5ftsPFxTBywEshvKUak4t0BE4AB-wtOnk0NAaJjuQCO5TImKJx8DXYwvnaikBiHeB5Z~QzsmeaCDOkcp982BoZD82ZQPFBAg1C1jIq2Zfz-nz8-6EkZj9uybRKv-vrs3DpiMmXnjM7HAgcZKrq7QDIRujLDpLDoP4kB-z7qOCdKR4oLixQ~~Pemk4gDqCIddO95o8VBWvPuL8x0CdpJrUNu-4Qq12eNMac15uKsTgYDwWPxqC8nVpZC3A0OfTQSmGw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Some_Weighted_Group_Algebras_are_Operator_Algebras","translated_slug":"","page_count":19,"language":"en","content_type":"Work","summary":"LetGbe a finitely generated group with polynomial growth, and letωbe a weight, i.e. a sub-multiplicative function onGwith positive values. We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 \u0026lt;α\u0026lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":83819313,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/83819313/thumbnails/1.jpg","file_name":"Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf","download_url":"https://www.academia.edu/attachments/83819313/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Weighted_Group_Algebras_are_Operato.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/83819313/Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf?1649706689=\u0026response-content-disposition=attachment%3B+filename%3DSome_Weighted_Group_Algebras_are_Operato.pdf\u0026Expires=1733907351\u0026Signature=ExKXoQuKMgJ3q3YBGEEsStXr3UbhAySxvb9pIAPsxi7rtTqDPx2ejiYLEzRHLsrYYpk2DwSOLG94Xm8Lrl~B5ftsPFxTBywEshvKUak4t0BE4AB-wtOnk0NAaJjuQCO5TImKJx8DXYwvnaikBiHeB5Z~QzsmeaCDOkcp982BoZD82ZQPFBAg1C1jIq2Zfz-nz8-6EkZj9uybRKv-vrs3DpiMmXnjM7HAgcZKrq7QDIRujLDpLDoP4kB-z7qOCdKR4oLixQ~~Pemk4gDqCIddO95o8VBWvPuL8x0CdpJrUNu-4Qq12eNMac15uKsTgYDwWPxqC8nVpZC3A0OfTQSmGw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> </div><div class="profile--tab_content_container js-tab-pane tab-pane" data-section-id="1583734" id="papers"><div class="js-work-strip profile--work_container" data-work-id="116584437"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/116584437/Beurling_Fourier_algebras_on_Lie_groups_and_their_spectra"><img alt="Research paper thumbnail of Beurling-Fourier algebras on Lie groups and their spectra" class="work-thumbnail" src="https://attachments.academia-assets.com/112673834/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/116584437/Beurling_Fourier_algebras_on_Lie_groups_and_their_spectra">Beurling-Fourier algebras on Lie groups and their spectra</a></div><div class="wp-workCard_item"><span>Advances in Mathematics</span><span>, 2021</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU (n), the Heisenberg group H, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover E(2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate "polynomially growing" weights does not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. CONTENTS 1. Introduction 2 1.1. Basic strategy 4 1.2. Organization 6 2. Preliminaries 6 2.1. Unbounded operators 6 2.1.1. Tensor products 8 2.1.2. Homomorphisms 8 2.1.3. Homomorphisms for non-commuting pairs 9 2.2. Lie groups, Lie algebras and related operators 9 2.3. Complexification of Lie groups 9 2.3.1. Operators associated to certain elements of the universal enveloping algebra and entire vectors 10 2.3.2. The choice of Fourier transforms 13 3. A refined definition for Beurling-Fourier algebras 13 3.1. Motivation: review of weights on abelian groups 13 3.2. Weights on the dual of G and Beurling-Fourier algebras 14 3.2.1. When W is bounded below 18 3.2.2. When G is separable and type I 19 3.3. Examples of weights 20 3.3.1. A list of weight functions on R k × Z n−k 20 3.3.2. Central weights 21 3.3.3. Extension from closed subgroups 23</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="097d0675385186b0484a7698b2b24831" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112673834,"asset_id":116584437,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112673834/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MCw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="116584437"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="116584437"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116584437; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116584437]").text(description); $(".js-view-count[data-work-id=116584437]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116584437; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116584437']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 116584437, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "097d0675385186b0484a7698b2b24831" } } $('.js-work-strip[data-work-id=116584437]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116584437,"title":"Beurling-Fourier algebras on Lie groups and their spectra","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"We investigate Beurling-Fourier algebras, a weighted version of Fourier algebras, on various Lie groups focusing on their spectral analysis. We will introduce a refined general definition of weights on the dual of locally compact groups and their associated Beurling-Fourier algebras. Constructions of nontrivial weights will be presented focusing on the cases of representative examples of Lie groups, namely SU (n), the Heisenberg group H, the reduced Heisenberg group Hr, the Euclidean motion group E(2) and its simply connected cover E(2). We will determine the spectrum of Beurling-Fourier algebras on each of the aforementioned groups emphasizing its connection to the complexification of underlying Lie groups. We also demonstrate \"polynomially growing\" weights does not change the spectrum and show the associated regularity of the resulting Beurling-Fourier algebras. CONTENTS 1. Introduction 2 1.1. Basic strategy 4 1.2. Organization 6 2. Preliminaries 6 2.1. Unbounded operators 6 2.1.1. Tensor products 8 2.1.2. Homomorphisms 8 2.1.3. Homomorphisms for non-commuting pairs 9 2.2. Lie groups, Lie algebras and related operators 9 2.3. Complexification of Lie groups 9 2.3.1. Operators associated to certain elements of the universal enveloping algebra and entire vectors 10 2.3.2. The choice of Fourier transforms 13 3. A refined definition for Beurling-Fourier algebras 13 3.1. Motivation: review of weights on abelian groups 13 3.2. Weights on the dual of G and Beurling-Fourier algebras 14 3.2.1. When W is bounded below 18 3.2.2. When G is separable and type I 19 3.3. Examples of weights 20 3.3.1. A list of weight functions on R k × Z n−k 20 3.3.2. Central weights 21 3.3.3. 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Lie groups, Lie algebras and related operators 9 2.3. Complexification of Lie groups 9 2.3.1. Operators associated to certain elements of the universal enveloping algebra and entire vectors 10 2.3.2. The choice of Fourier transforms 13 3. A refined definition for Beurling-Fourier algebras 13 3.1. Motivation: review of weights on abelian groups 13 3.2. Weights on the dual of G and Beurling-Fourier algebras 14 3.2.1. When W is bounded below 18 3.2.2. When G is separable and type I 19 3.3. Examples of weights 20 3.3.1. A list of weight functions on R k × Z n−k 20 3.3.2. Central weights 21 3.3.3. 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The question of when a weighted Fourier algebra on G G ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G G be a compact connected Lie group. The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of the Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d1192d6bdf37e678757263ec4c63ed9b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112673808,"asset_id":116584436,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112673808/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="116584436"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="116584436"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116584436; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116584436]").text(description); $(".js-view-count[data-work-id=116584436]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116584436; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116584436']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 116584436, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d1192d6bdf37e678757263ec4c63ed9b" } } $('.js-work-strip[data-work-id=116584436]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116584436,"title":"Some Beurling–Fourier algebras on compact groups are operator algebras","translated_title":"","metadata":{"abstract":"Let G G be a compact connected Lie group. The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. 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The question of when a weighted Fourier algebra on G G is completely isomorphic to an operator algebra will be investigated in this paper. We will demonstrate that the dimension of the group plays an important role in the question. More precisely, we will get a positive answer to the question when we consider a polynomial type weight coming from a length function on G G with the order of growth strictly bigger than half of the dimension of the group. The case of S U ( n ) SU(n) will be examined, focusing more on the details including negative results. The proof for the positive directions depends on a non-commutative version of the Littlewood multiplier theory, which we will develop in this paper, and the negative directions will be taken care of by restricting to a maximal torus.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":112673808,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673808/thumbnails/1.jpg","file_name":"S0002-9947-2015-06653-7.pdf","download_url":"https://www.academia.edu/attachments/112673808/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Beurling_Fourier_algebras_on_compac.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673808/S0002-9947-2015-06653-7-libre.pdf?1711188579=\u0026response-content-disposition=attachment%3B+filename%3DSome_Beurling_Fourier_algebras_on_compac.pdf\u0026Expires=1733907351\u0026Signature=GuoIuJQPxyHcWtjewQJh4cnOPCoF5jCmrjDM7Ml7opNE2b-9-ccdTTOn5wPQImMUaQOa7zAvRMCd3wj1VH1PEnpMQXfIQ0YH3beE2z42UFX1~v0OZZ5wJYmx66Zjk92qUADWXLN3SLHw2t25h7dz~BSLoTDklsCe0n8ulgA1ZthB0968UNE5e9YY7vdQTuN~SrxpaIrwHGaz0oVDfARS85HT0vwoXWGNJhuFTRx52x1cFal0lWkD1nJIqWsEAUh-cMtATsB3a3dZlURYjNMp~MuD1LkNfrNmT98jvJxAOv9ebmT9jj~jZGyOn0EZf1S3VhtcYTKE3ES8J~~r73Ppqg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":112673809,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673809/thumbnails/1.jpg","file_name":"S0002-9947-2015-06653-7.pdf","download_url":"https://www.academia.edu/attachments/112673809/download_file","bulk_download_file_name":"Some_Beurling_Fourier_algebras_on_compac.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673809/S0002-9947-2015-06653-7-libre.pdf?1711188581=\u0026response-content-disposition=attachment%3B+filename%3DSome_Beurling_Fourier_algebras_on_compac.pdf\u0026Expires=1733907351\u0026Signature=HBCCeRpveHIACDxcFQt4-nijTpL3M7AJPrQxnl1US~S1fmLbh112xZyeV2-8zBJ~~TdJDUeO2kgwow~6lHORuMoW2vaHPiB0NvjGPa0XtXHNW47M6H5XeWVC98WlctWlR4MZPSIV-GSQHfkFE-~xqeEIU5UAMYtzbT64iMUDSwfza9Kwm5XpADlla91amlChhFcBWXenb~s2mS0m-qyIFX4eVS7BvzelwOJziczEHxVaRSFBztzmNI8CO~1zHqryGuJpFHAXfH8gtlSKZkL7bLF5JNAK17fQ-vwC7y6xkLEnVjKN4n6uu4gICkQKEjrEjwB8oq~ceal3X9R7eYmIAQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":26817,"name":"Algorithm","url":"https://www.academia.edu/Documents/in/Algorithm"},{"id":38072,"name":"Annotation","url":"https://www.academia.edu/Documents/in/Annotation"}],"urls":[{"id":40541368,"url":"http://www.ams.org/tran/2015-367-10/S0002-9947-2015-06653-7/S0002-9947-2015-06653-7.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="116584430"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/116584430/Corrigendum_Similarity_degree_of_Fourier_algebras"><img alt="Research paper thumbnail of Corrigendum: Similarity degree of Fourier algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/112673830/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/116584430/Corrigendum_Similarity_degree_of_Fourier_algebras">Corrigendum: Similarity degree of Fourier algebras</a></div><div class="wp-workCard_item"><span>Journal of Functional Analysis</span><span>, 2018</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes the matricial open unit ball b 1 (M n ⊗ V 0) onto b 1 (M n ⊗ [V 0 /(V 0 ∩ W)]) ∼ = b 1 ([M n ⊗ V 0 ]/[M n ⊗ (V 0 ∩ W)]). We now recall the notation of [7]. For a Banach algebra and operator space A, c ≥ 1, A c (contained in B(H c)) is the universal operator algebra generated by representations on Hilbert spaces π : A → B(H) with completely bounded norm π cb ≤ c, and ι c : A → A c is the canonical embedding. Note that we assume that ι 1 is injective. We say that A satisfies the similarity property for completely bounded homomorphims if for each completely bounded homomorphim π : A → B(H), there is an invertible S in B(H) for which Sπ(•)S −1 cb ≤ 1. We also consider the "weighted multiplication" map on the N-fold Haagerup tensor product of A with itself, m N,c : A N ⊗ h → A c , given on elementary tensor by m N,c (u 1 ⊗ • • • ⊗ u N) = 1 c N ι c (u 1). .. ι c (u n) = 1 c N ι c (u 1 ,. .. u N) which is a complete contraction.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9d5648fc1e191a3f869a575b799d2225" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":112673830,"asset_id":116584430,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/112673830/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="116584430"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="116584430"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 116584430; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=116584430]").text(description); $(".js-view-count[data-work-id=116584430]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 116584430; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='116584430']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 116584430, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "9d5648fc1e191a3f869a575b799d2225" } } $('.js-work-strip[data-work-id=116584430]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":116584430,"title":"Corrigendum: Similarity degree of Fourier algebras","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes the matricial open unit ball b 1 (M n ⊗ V 0) onto b 1 (M n ⊗ [V 0 /(V 0 ∩ W)]) ∼ = b 1 ([M n ⊗ V 0 ]/[M n ⊗ (V 0 ∩ W)]). We now recall the notation of [7]. For a Banach algebra and operator space A, c ≥ 1, A c (contained in B(H c)) is the universal operator algebra generated by representations on Hilbert spaces π : A → B(H) with completely bounded norm π cb ≤ c, and ι c : A → A c is the canonical embedding. Note that we assume that ι 1 is injective. We say that A satisfies the similarity property for completely bounded homomorphims if for each completely bounded homomorphim π : A → B(H), there is an invertible S in B(H) for which Sπ(•)S −1 cb ≤ 1. We also consider the \"weighted multiplication\" map on the N-fold Haagerup tensor product of A with itself, m N,c : A N ⊗ h → A c , given on elementary tensor by m N,c (u 1 ⊗ • • • ⊗ u N) = 1 c N ι c (u 1). .. ι c (u n) = 1 c N ι c (u 1 ,. .. u N) which is a complete contraction.","publication_date":{"day":null,"month":null,"year":2018,"errors":{}},"publication_name":"Journal of Functional Analysis","grobid_abstract_attachment_id":112673830},"translated_abstract":null,"internal_url":"https://www.academia.edu/116584430/Corrigendum_Similarity_degree_of_Fourier_algebras","translated_internal_url":"","created_at":"2024-03-23T02:37:55.040-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":112673830,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673830/thumbnails/1.jpg","file_name":"1808.pdf","download_url":"https://www.academia.edu/attachments/112673830/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Corrigendum_Similarity_degree_of_Fourier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673830/1808-libre.pdf?1711188562=\u0026response-content-disposition=attachment%3B+filename%3DCorrigendum_Similarity_degree_of_Fourier.pdf\u0026Expires=1733907351\u0026Signature=LqcVTwfojhmFwyA9S4o0pEtfXlw9SKGfRFS2E0OFSEuwAGYAYgJ5fjIozcNO0nTYP93IKKQLbhc4QDMvmD17iNp1jtq06~pOcg7NK~FE~XZefQCOsqUMaElxu5yPy3iVwH8r9D29NdJw1fvMmzYuwdLEBoCSATFEg9p0PL9tqvOJHCZI81TPuyRJ6lrNhpgMul3rhNLnGvun8V8MTBk~WJM820C969Os3kGt9huowyXbS56e-5HyRSrrIkdxGbTXcxSvIdb-1V1KpiIprla078z95FtR0C8q~szSRe9Dbnm2PPsKs9c4Tdpw6dy1F9N89NU3Tg0Qtf3QJPzpVAl52A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Corrigendum_Similarity_degree_of_Fourier_algebras","translated_slug":"","page_count":6,"language":"en","content_type":"Work","summary":"Hence we identify V 0 /(V 0 ∩ W) as a subspace of V/W and, for any n ∈ N, the quotient map takes the matricial open unit ball b 1 (M n ⊗ V 0) onto b 1 (M n ⊗ [V 0 /(V 0 ∩ W)]) ∼ = b 1 ([M n ⊗ V 0 ]/[M n ⊗ (V 0 ∩ W)]). We now recall the notation of [7]. For a Banach algebra and operator space A, c ≥ 1, A c (contained in B(H c)) is the universal operator algebra generated by representations on Hilbert spaces π : A → B(H) with completely bounded norm π cb ≤ c, and ι c : A → A c is the canonical embedding. Note that we assume that ι 1 is injective. We say that A satisfies the similarity property for completely bounded homomorphims if for each completely bounded homomorphim π : A → B(H), there is an invertible S in B(H) for which Sπ(•)S −1 cb ≤ 1. We also consider the \"weighted multiplication\" map on the N-fold Haagerup tensor product of A with itself, m N,c : A N ⊗ h → A c , given on elementary tensor by m N,c (u 1 ⊗ • • • ⊗ u N) = 1 c N ι c (u 1). .. ι c (u n) = 1 c N ι c (u 1 ,. .. u N) which is a complete contraction.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":112673830,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/112673830/thumbnails/1.jpg","file_name":"1808.pdf","download_url":"https://www.academia.edu/attachments/112673830/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Corrigendum_Similarity_degree_of_Fourier.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/112673830/1808-libre.pdf?1711188562=\u0026response-content-disposition=attachment%3B+filename%3DCorrigendum_Similarity_degree_of_Fourier.pdf\u0026Expires=1733907351\u0026Signature=LqcVTwfojhmFwyA9S4o0pEtfXlw9SKGfRFS2E0OFSEuwAGYAYgJ5fjIozcNO0nTYP93IKKQLbhc4QDMvmD17iNp1jtq06~pOcg7NK~FE~XZefQCOsqUMaElxu5yPy3iVwH8r9D29NdJw1fvMmzYuwdLEBoCSATFEg9p0PL9tqvOJHCZI81TPuyRJ6lrNhpgMul3rhNLnGvun8V8MTBk~WJM820C969Os3kGt9huowyXbS56e-5HyRSrrIkdxGbTXcxSvIdb-1V1KpiIprla078z95FtR0C8q~szSRe9Dbnm2PPsKs9c4Tdpw6dy1F9N89NU3Tg0Qtf3QJPzpVAl52A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":390056,"name":"Fourier transform","url":"https://www.academia.edu/Documents/in/Fourier_transform"},{"id":1713495,"name":"Degree in music","url":"https://www.academia.edu/Documents/in/Degree_in_music"},{"id":3847659,"name":"Similarity Geometry","url":"https://www.academia.edu/Documents/in/Similarity_Geometry"}],"urls":[{"id":40541366,"url":"https://api.elsevier.com/content/article/PII:S0022123618303914?httpAccept=text/xml"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982388"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982388/Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity"><img alt="Research paper thumbnail of Beurling-Fourier algebras, operator amenability and Arens regularity" class="work-thumbnail" src="https://attachments.academia-assets.com/82302097/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982388/Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity">Beurling-Fourier algebras, operator amenability and Arens regularity</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="5c488adb6f636d9c030302047b4779df" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302097,"asset_id":73982388,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302097/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982388"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982388"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982388; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982388]").text(description); $(".js-view-count[data-work-id=73982388]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982388; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982388']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982388, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "5c488adb6f636d9c030302047b4779df" } } $('.js-work-strip[data-work-id=73982388]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982388,"title":"Beurling-Fourier algebras, operator amenability and Arens regularity","translated_title":"","metadata":{"abstract":"We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).","publication_date":{"day":1,"month":9,"year":2010,"errors":{}}},"translated_abstract":"We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).","internal_url":"https://www.academia.edu/73982388/Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity","translated_internal_url":"","created_at":"2022-03-17T21:40:37.750-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302097,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302097/thumbnails/1.jpg","file_name":"1009.0094.pdf","download_url":"https://www.academia.edu/attachments/82302097/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Beurling_Fourier_algebras_operator_amena.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302097/1009.0094-libre.pdf?1647582028=\u0026response-content-disposition=attachment%3B+filename%3DBeurling_Fourier_algebras_operator_amena.pdf\u0026Expires=1733907351\u0026Signature=a~mMOQZhs02zua8J1q66Z5ViDuQJ3zCGw8ChRDoXraXWbAIooX8-9~IsOHBRYxv9mJaufrTEArU2znRycuiHaUnmSAvbLQnEWyYalQaa1GLpZoPaPeH4h3YIDGpFufcVLd6y1-vbrtHEcimyGPObYOncDFsvCs9lixUH-5wb-x7zD6nyvoMxeP-lbMQayGejE2erZ6kAzGm1WBNO0EOuV0NPgVwRJGZM-WBxdLXd3AW4JjBb2x-3etyw9wWHax9HSRl43RodgJC1vQp93ij71jmKuXhbdalSxRsO~lrHfSQg48jrj25~0umw9va4wz1GVjdb59JelUgpggfhCHhfaA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Beurling_Fourier_algebras_operator_amenability_and_Arens_regularity","translated_slug":"","page_count":42,"language":"en","content_type":"Work","summary":"We introduce the class of Beurling-Fourier algebras on locally compact groups and show that they are non-commutative analogs of classical Beurling algebras. We obtain various results with regard to the operator amenability, operator weak amenability and Arens regularity of Beurling-Fourier algebras on compact groups and show that they behave very similarly to the classical Beurling algebras of discrete groups. We then apply our results to study explicitly the Beurling-Fourier algebras on SU(2), the 2 × 2 unitary group. We demonstrate that how Beurling-Fourier algebras are closely connected to the amenability of the Fourier algebra of SU(2). Another major consequence of our results is that our investigation allows us to construct families of unital infinite-dimensional closed Arens regular subalgebras of the Fourier algebra of certain products of SU(2).","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302097,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302097/thumbnails/1.jpg","file_name":"1009.0094.pdf","download_url":"https://www.academia.edu/attachments/82302097/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Beurling_Fourier_algebras_operator_amena.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302097/1009.0094-libre.pdf?1647582028=\u0026response-content-disposition=attachment%3B+filename%3DBeurling_Fourier_algebras_operator_amena.pdf\u0026Expires=1733907351\u0026Signature=a~mMOQZhs02zua8J1q66Z5ViDuQJ3zCGw8ChRDoXraXWbAIooX8-9~IsOHBRYxv9mJaufrTEArU2znRycuiHaUnmSAvbLQnEWyYalQaa1GLpZoPaPeH4h3YIDGpFufcVLd6y1-vbrtHEcimyGPObYOncDFsvCs9lixUH-5wb-x7zD6nyvoMxeP-lbMQayGejE2erZ6kAzGm1WBNO0EOuV0NPgVwRJGZM-WBxdLXd3AW4JjBb2x-3etyw9wWHax9HSRl43RodgJC1vQp93ij71jmKuXhbdalSxRsO~lrHfSQg48jrj25~0umw9va4wz1GVjdb59JelUgpggfhCHhfaA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302096,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302096/thumbnails/1.jpg","file_name":"1009.0094.pdf","download_url":"https://www.academia.edu/attachments/82302096/download_file","bulk_download_file_name":"Beurling_Fourier_algebras_operator_amena.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302096/1009.0094-libre.pdf?1647582028=\u0026response-content-disposition=attachment%3B+filename%3DBeurling_Fourier_algebras_operator_amena.pdf\u0026Expires=1733907351\u0026Signature=dPSK62FoKcD6z9-UmULfgDXRJcNwXUWkY5fyYFd7kWCLkG7~pl90Dix85NDr-ebUElxffGWfsZqZnNY4FRbNqSlacUcWoaAq2fJb9TYGWM3zKh1kZ4ydXmV-pgUiGzAYgkc~ntGmb1ib16L~Vlwkl~XIOnOgzf87mpjmS~F0N1Ux9BzNc6wJIfKFvSbUk0qI6i-MGP6ejNt4JWVbYS4MSgzTxVbxnnSl1d3oyy3N7e56~Dpe-~aCTsC5xjgPzf2tq0rKXM-IxPgqJK6S9oafSgdT~qAgcJsdSLH6VH3iLFtx2wwAr0p78PUbzoRf91RYRL-MC6ivclnGaA1dQOfYaw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"},{"id":2756578,"name":"Unitary group","url":"https://www.academia.edu/Documents/in/Unitary_group"}],"urls":[{"id":18589301,"url":"https://archive.org/download/arxiv-1009.0094/1009.0094.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982387"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982387/Similarity_degree_of_Fourier_algebras"><img alt="Research paper thumbnail of Similarity degree of Fourier algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/82302100/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982387/Similarity_degree_of_Fourier_algebras">Similarity degree of Fourier algebras</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that for a locally compact group G, amongst a class which contains amenable and small inv...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier&#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6d62dd583568f2389e9ea569ac67827b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302100,"asset_id":73982387,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302100/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982387"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982387"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982387; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982387]").text(description); $(".js-view-count[data-work-id=73982387]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982387; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982387']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982387, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6d62dd583568f2389e9ea569ac67827b" } } $('.js-work-strip[data-work-id=73982387]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982387,"title":"Similarity degree of Fourier algebras","translated_title":"","metadata":{"abstract":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier\u0026#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.","publication_date":{"day":18,"month":3,"year":2016,"errors":{}}},"translated_abstract":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier\u0026#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.","internal_url":"https://www.academia.edu/73982387/Similarity_degree_of_Fourier_algebras","translated_internal_url":"","created_at":"2022-03-17T21:40:37.557-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302100,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302100/thumbnails/1.jpg","file_name":"1511.03423v3.pdf","download_url":"https://www.academia.edu/attachments/82302100/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Similarity_degree_of_Fourier_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302100/1511.03423v3-libre.pdf?1647582022=\u0026response-content-disposition=attachment%3B+filename%3DSimilarity_degree_of_Fourier_algebras.pdf\u0026Expires=1733907351\u0026Signature=TBLRxoYpZd2OT5dWIV~DEMhlV5lQygJp9zdxLwnEwqkaQzT6-DIjhp8xQ5BWTb5CiLHNz-zzdNpb6AtPjui7sSPHBZNWaQsFOlLv2Jo6pIZwg565lR9PXy0ThDfrPDP2h6gNuLIq1RXak3VMD16SNr5uS7hY~XlvkAWE6U8FOeITXtSzom-xdgJD46NoN77XuZCBrRwGV7nJ8EZVs7eszrhdZfrElb7BVxDBSF5rQVHQpKKLEUZecu3p9BoB9~9pS2h0r7nECpPU-2xm5NuqS6WraBmhAEGYQUIrvPS45P5fx2orI7ySwTSYrKjfNrEOadP0F09RoJhPRdMRL5iB1A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Similarity_degree_of_Fourier_algebras","translated_slug":"","page_count":14,"language":"en","content_type":"Work","summary":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier\u0026#39;s similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π: A(G)→ B(H) admits an invertible S in B(H) for which SS^-1≤ ||π||_cb^2 and S^-1π(·)S extends to a *-representation of the C^*-algebra C_0(G). This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (Münster J. Math 6, 2013). We also note that A(G) has completely bounded similarity degree 1 if and only if it is completely isomorphic to an operator algebra if and only if G is finite.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302100,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302100/thumbnails/1.jpg","file_name":"1511.03423v3.pdf","download_url":"https://www.academia.edu/attachments/82302100/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Similarity_degree_of_Fourier_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302100/1511.03423v3-libre.pdf?1647582022=\u0026response-content-disposition=attachment%3B+filename%3DSimilarity_degree_of_Fourier_algebras.pdf\u0026Expires=1733907351\u0026Signature=TBLRxoYpZd2OT5dWIV~DEMhlV5lQygJp9zdxLwnEwqkaQzT6-DIjhp8xQ5BWTb5CiLHNz-zzdNpb6AtPjui7sSPHBZNWaQsFOlLv2Jo6pIZwg565lR9PXy0ThDfrPDP2h6gNuLIq1RXak3VMD16SNr5uS7hY~XlvkAWE6U8FOeITXtSzom-xdgJD46NoN77XuZCBrRwGV7nJ8EZVs7eszrhdZfrElb7BVxDBSF5rQVHQpKKLEUZecu3p9BoB9~9pS2h0r7nECpPU-2xm5NuqS6WraBmhAEGYQUIrvPS45P5fx2orI7ySwTSYrKjfNrEOadP0F09RoJhPRdMRL5iB1A__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589300,"url":"https://arxiv.org/pdf/1511.03423v3.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982386"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982386/Distance_k_graphs_of_hypercube_and_q_Hermite_polynomials"><img alt="Research paper thumbnail of Distance k-graphs of hypercube and q-Hermite polynomials" class="work-thumbnail" src="https://attachments.academia-assets.com/82302095/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982386/Distance_k_graphs_of_hypercube_and_q_Hermite_polynomials">Distance k-graphs of hypercube and q-Hermite polynomials</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We will prove that some weighted graphs on the distance k-graph of hypercubes approximate the q-H...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We will prove that some weighted graphs on the distance k-graph of hypercubes approximate the q-Hermite polynomial of a q-gaussian variable by providing an appropriate matrix model.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="9f33433b4e75c6b1050c226001e70c6c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302095,"asset_id":73982386,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302095/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982386"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982386"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982386; 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982385"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982385/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups"><img alt="Research paper thumbnail of New deformations of Convolution algebras and Fourier algebras on locally compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/82302094/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982385/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups">New deformations of Convolution algebras and Fourier algebras on locally compact groups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on lo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4d6a0e0da51340c1203877ada2ae2ec7" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302094,"asset_id":73982385,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302094/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982385"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982385"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982385; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982385]").text(description); $(".js-view-count[data-work-id=73982385]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982385; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982385']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982385, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4d6a0e0da51340c1203877ada2ae2ec7" } } $('.js-work-strip[data-work-id=73982385]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982385,"title":"New deformations of Convolution algebras and Fourier algebras on locally compact groups","translated_title":"","metadata":{"abstract":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.","publication_date":{"day":5,"month":8,"year":2015,"errors":{}}},"translated_abstract":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. 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Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.","internal_url":"https://www.academia.edu/73982385/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups","translated_internal_url":"","created_at":"2022-03-17T21:40:37.184-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302094,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302094/thumbnails/1.jpg","file_name":"1508.01092v1.pdf","download_url":"https://www.academia.edu/attachments/82302094/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"New_deformations_of_Convolution_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302094/1508.01092v1-libre.pdf?1647582023=\u0026response-content-disposition=attachment%3B+filename%3DNew_deformations_of_Convolution_algebras.pdf\u0026Expires=1733907351\u0026Signature=Bred7TZfZV7ybjXNHD1YtEFekAQeapUrneWwoHTs5B00YvQkSqfXSMCrqSV-P3sSb8amwfAbTmlD37F48PA40YsEARxNb-vJgO5~lxSvZiVM97VSepkSYx9dqhePAhijyZxCrPxSjhj3z2~oXtlJk6sYWX6--EeRbxBrVqzYZZS7uYsyWo9VrTA8qFefxyOaKYVTUZ-4dlvNpOYDioG0ujmtI0xEV1HC~FGOiUcPKSIFZjUfof0L-mR1J2vG19NfyzzE1c3SnCrZqZwd0uwkGRIQe7tDvj9A1IcGsVZo9I~CzJaJU~9-07zem8-JKjXFq3TkfPBWaEEB5Kjesf~rRQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups","translated_slug":"","page_count":17,"language":"en","content_type":"Work","summary":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. 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For a fixed k&gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d081ded98cd423f67190286fbf29ab41" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302093,"asset_id":73982384,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302093/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982384"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982384"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982384; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982384]").text(description); $(".js-view-count[data-work-id=73982384]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982384; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982384']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982384, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d081ded98cd423f67190286fbf29ab41" } } $('.js-work-strip[data-work-id=73982384]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982384,"title":"Asymptotic Spectral Distributions of Distance k-Graphs of Cartesian Product Graphs","translated_title":"","metadata":{"abstract":"Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k\u0026gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","publication_date":{"day":8,"month":4,"year":2013,"errors":{}}},"translated_abstract":"Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k\u0026gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","internal_url":"https://www.academia.edu/73982384/Asymptotic_Spectral_Distributions_of_Distance_k_Graphs_of_Cartesian_Product_Graphs","translated_internal_url":"","created_at":"2022-03-17T21:40:36.998-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302093,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302093/thumbnails/1.jpg","file_name":"1304.1236.pdf","download_url":"https://www.academia.edu/attachments/82302093/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotic_Spectral_Distributions_of_Dis.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302093/1304.1236-libre.pdf?1647582023=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotic_Spectral_Distributions_of_Dis.pdf\u0026Expires=1733907351\u0026Signature=QOvFgdYPdXuRJvAP4OL4xyHgdplIk11qJ3ubPBE5n~~iwq6NqkeHdGGXGdBXpZf4A08gENacUXV1PI2w6Vuwl8iRttdlNT3rub7ZXv91-1HKXDm0LaiBL1vUlY2a~gD11PyzR9I31uxjeDoh0yY0dLTcH3GiXTtnN-4~x3gvnI8R0uWzRPc0rSBPTWo3N6RRaQi09wzvjBXzbfrZoPCEoFksq7LPYWwZkUcPn9gpzYi4FF3lSwOB5i80nNnX2qKHRhFNFu7dUW7TCdqGRmiilT~lCtosDzznWyprQ3yOznglLoGCBBC91sCRL3cK76GGwiQS2fPDhzZf1C~AZ2WcbQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Asymptotic_Spectral_Distributions_of_Distance_k_Graphs_of_Cartesian_Product_Graphs","translated_slug":"","page_count":13,"language":"en","content_type":"Work","summary":"Let G be a finite connected graph on two or more vertices and G^[N,k] the distance k-graph of the N-fold Cartesian power of G. For a fixed k\u0026gt;1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G^[N,k]. The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302093,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302093/thumbnails/1.jpg","file_name":"1304.1236.pdf","download_url":"https://www.academia.edu/attachments/82302093/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Asymptotic_Spectral_Distributions_of_Dis.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302093/1304.1236-libre.pdf?1647582023=\u0026response-content-disposition=attachment%3B+filename%3DAsymptotic_Spectral_Distributions_of_Dis.pdf\u0026Expires=1733907351\u0026Signature=QOvFgdYPdXuRJvAP4OL4xyHgdplIk11qJ3ubPBE5n~~iwq6NqkeHdGGXGdBXpZf4A08gENacUXV1PI2w6Vuwl8iRttdlNT3rub7ZXv91-1HKXDm0LaiBL1vUlY2a~gD11PyzR9I31uxjeDoh0yY0dLTcH3GiXTtnN-4~x3gvnI8R0uWzRPc0rSBPTWo3N6RRaQi09wzvjBXzbfrZoPCEoFksq7LPYWwZkUcPn9gpzYi4FF3lSwOB5i80nNnX2qKHRhFNFu7dUW7TCdqGRmiilT~lCtosDzznWyprQ3yOznglLoGCBBC91sCRL3cK76GGwiQS2fPDhzZf1C~AZ2WcbQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589297,"url":"https://archive.org/download/arxiv-1304.1236/1304.1236.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982382"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982382/p_Fourier_algebras_on_compact_groups"><img alt="Research paper thumbnail of p-Fourier algebras on compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/82302099/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982382/p_Fourier_algebras_on_compact_groups">p-Fourier algebras on compact groups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p&gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="228fd10866ad5e7b8cbc852b69b05e72" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302099,"asset_id":73982382,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302099/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982382"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982382"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982382; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982382]").text(description); $(".js-view-count[data-work-id=73982382]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982382; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982382']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982382, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "228fd10866ad5e7b8cbc852b69b05e72" } } $('.js-work-strip[data-work-id=73982382]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982382,"title":"p-Fourier algebras on compact groups","translated_title":"","metadata":{"abstract":"Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p\u0026gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.","publication_date":{"day":17,"month":2,"year":2015,"errors":{}}},"translated_abstract":"Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p\u0026gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.","internal_url":"https://www.academia.edu/73982382/p_Fourier_algebras_on_compact_groups","translated_internal_url":"","created_at":"2022-03-17T21:40:36.812-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302099/thumbnails/1.jpg","file_name":"1411.2336v2.pdf","download_url":"https://www.academia.edu/attachments/82302099/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"p_Fourier_algebras_on_compact_groups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302099/1411.2336v2-libre.pdf?1647582030=\u0026response-content-disposition=attachment%3B+filename%3Dp_Fourier_algebras_on_compact_groups.pdf\u0026Expires=1733907351\u0026Signature=Bj2vKT3H0UdNkA4XTGAac-EPikngssb7N3Ata0LGCKDBW7h99fO3SWb5HXJE1dDyIfYM6~tWqlSm2L8H0XkZgWOnRsgUSFLcymH1h8QksiMhkZZtV6vczknx5DQmOuc3tzG5SfEonovGCFY6E1Az8B8SKwnfBtJ7~sMtMnfBycoaSGtZkzo0ZBdl7CedpBpeOR0~9LAT8iNxGj8lMlZvLWHEw-wzeXmueJeeejYggg~XToep5llXhaJ2uv67PJZsz~2Kwm6vMc0MuaufkA61up-Mp1lmFaWtUEuTIg8VOtpaIYMvpa2qPIH8etJlLDMJWr6LZBPEGwjQrgpxG9oC7g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"p_Fourier_algebras_on_compact_groups","translated_slug":"","page_count":41,"language":"en","content_type":"Work","summary":"Let G be a compact group. For 1≤ p≤∞ we introduce a class of Banach function algebras A^p(G) on G which are the Fourier algebras in the case p=1, and for p=2 are certain algebras discovered in forrestss1. In the case p=2 we find that A^p(G)A^p(H) if and only if G and H are isomorphic compact groups. These algebras admit natural operator space structures, and also weighted versions, which we call p-Beurling-Fourier algebras. We study various amenability and operator amenability properties, Arens regularity and representability as operator algebras. For a connected Lie G and p\u0026gt;1, our techniques of estimation of when certain p-Beurling-Fourier algebras are operator algebras rely more on the fine structure of G, than in the case p=1. We also study restrictions to subgroups. In the case that G=SU(2), restrict to a torus and obtain some exotic algebras of Laurent series. We study amenability properties of these new algebras, as well.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302099,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302099/thumbnails/1.jpg","file_name":"1411.2336v2.pdf","download_url":"https://www.academia.edu/attachments/82302099/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"p_Fourier_algebras_on_compact_groups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302099/1411.2336v2-libre.pdf?1647582030=\u0026response-content-disposition=attachment%3B+filename%3Dp_Fourier_algebras_on_compact_groups.pdf\u0026Expires=1733907351\u0026Signature=Bj2vKT3H0UdNkA4XTGAac-EPikngssb7N3Ata0LGCKDBW7h99fO3SWb5HXJE1dDyIfYM6~tWqlSm2L8H0XkZgWOnRsgUSFLcymH1h8QksiMhkZZtV6vczknx5DQmOuc3tzG5SfEonovGCFY6E1Az8B8SKwnfBtJ7~sMtMnfBycoaSGtZkzo0ZBdl7CedpBpeOR0~9LAT8iNxGj8lMlZvLWHEw-wzeXmueJeeejYggg~XToep5llXhaJ2uv67PJZsz~2Kwm6vMc0MuaufkA61up-Mp1lmFaWtUEuTIg8VOtpaIYMvpa2qPIH8etJlLDMJWr6LZBPEGwjQrgpxG9oC7g__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302098,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302098/thumbnails/1.jpg","file_name":"1411.2336v2.pdf","download_url":"https://www.academia.edu/attachments/82302098/download_file","bulk_download_file_name":"p_Fourier_algebras_on_compact_groups.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302098/1411.2336v2-libre.pdf?1647582030=\u0026response-content-disposition=attachment%3B+filename%3Dp_Fourier_algebras_on_compact_groups.pdf\u0026Expires=1733907351\u0026Signature=DhSA~S0h0E3bH6tLrYPjinKbbojM3fJ0R64L6XE~i1geR8jnUqrn7b9NM7-i65VpDjsSnbrNah12YudltXveE0KfyxiGu2omrZr0j-O5YX8s8ZfhXhwmDQkcX1u-EWXwuPAB7AgY24aUQNQKApx6v0zFBPjPNuF7D56JykP2XXta7qQrVUz6SPCOtX9NwdKK6yBK6KgyZVyYnZ2nszbcb8ItkEQL-6ez~bpB1349n6MHFtj7m8OGyGmnlreVYwyQDN5FAZnn4cPg2KPb5jinL1zCawQlP5GzJEFBgvfNBsfPsZ6li2h2Zy0o7~8uhuCovEbi1fBFhS94CL7mLe0Arw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589295,"url":"https://arxiv.org/pdf/1411.2336v2.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982380"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982380/Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras"><img alt="Research paper thumbnail of Integration over the quantum diagonal subgroup and associated Fourier-like algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/82302087/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982380/Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras">Integration over the quantum diagonal subgroup and associated Fourier-like algebras</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N&gt; 2, associated to Wang&#39;s free orthogonal groups, and show that they are not operator weakly amenable.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="d46de7c3b05b20a66d24a78c5f3b999b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302087,"asset_id":73982380,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302087/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982380"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982380"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982380; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982380]").text(description); $(".js-view-count[data-work-id=73982380]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982380; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982380']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982380, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d46de7c3b05b20a66d24a78c5f3b999b" } } $('.js-work-strip[data-work-id=73982380]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982380,"title":"Integration over the quantum diagonal subgroup and associated Fourier-like algebras","translated_title":"","metadata":{"abstract":"By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N\u0026gt; 2, associated to Wang\u0026#39;s free orthogonal groups, and show that they are not operator weakly amenable.","publication_date":{"day":15,"month":6,"year":2016,"errors":{}}},"translated_abstract":"By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N\u0026gt; 2, associated to Wang\u0026#39;s free orthogonal groups, and show that they are not operator weakly amenable.","internal_url":"https://www.academia.edu/73982380/Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras","translated_internal_url":"","created_at":"2022-03-17T21:40:36.627-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302087,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302087/thumbnails/1.jpg","file_name":"1605.02705v2.pdf","download_url":"https://www.academia.edu/attachments/82302087/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Integration_over_the_quantum_diagonal_su.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302087/1605.02705v2-libre.pdf?1647582027=\u0026response-content-disposition=attachment%3B+filename%3DIntegration_over_the_quantum_diagonal_su.pdf\u0026Expires=1733907351\u0026Signature=C7v2TOmyXFJJYCCaHJrBWbZcsv72Ctx7TjjYdJvA2Sq9MVBIJdNeOBvGrrXM8K5kaYsvBGwXcNnnqDD9uM0XbbrLepjIgv~2z~Hf8MKOClhvzE5Bh3VmWqJc8BfW16dOlUgRK3401zR0HKivF5aiRqoYfmpVahas~Xsl3SnyLCVFx~I5Tw06~fB3lOBCp6q3I2Nao8TOg3I6e0ow-yhduxd~V~JPtJUY6-BzlZwSW1AApCUJUq9y2jQyGpAeRVK97PZeQYagR60HlrLVWZuKXez0uK3j6Kca09saPFGh9eiqvOOkgV2AWPNl4meRG7U-dQD81FI~ydIiLMJhAugBUA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Integration_over_the_quantum_diagonal_subgroup_and_associated_Fourier_like_algebras","translated_slug":"","page_count":31,"language":"en","content_type":"Work","summary":"By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group G a completely contractive Banach algebra A_Δ(G), which can be viewed as a deformed Fourier algebra of G. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and Sołtan, the corresponding integration represented by a certain idempotent state on C(G) makes sense as long as G is of Kac type. Finally we analyse as an explicit example the algebras A_Δ(O_N^+), N\u0026gt; 2, associated to Wang\u0026#39;s free orthogonal groups, and show that they are not operator weakly amenable.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302087,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302087/thumbnails/1.jpg","file_name":"1605.02705v2.pdf","download_url":"https://www.academia.edu/attachments/82302087/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Integration_over_the_quantum_diagonal_su.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302087/1605.02705v2-libre.pdf?1647582027=\u0026response-content-disposition=attachment%3B+filename%3DIntegration_over_the_quantum_diagonal_su.pdf\u0026Expires=1733907351\u0026Signature=C7v2TOmyXFJJYCCaHJrBWbZcsv72Ctx7TjjYdJvA2Sq9MVBIJdNeOBvGrrXM8K5kaYsvBGwXcNnnqDD9uM0XbbrLepjIgv~2z~Hf8MKOClhvzE5Bh3VmWqJc8BfW16dOlUgRK3401zR0HKivF5aiRqoYfmpVahas~Xsl3SnyLCVFx~I5Tw06~fB3lOBCp6q3I2Nao8TOg3I6e0ow-yhduxd~V~JPtJUY6-BzlZwSW1AApCUJUq9y2jQyGpAeRVK97PZeQYagR60HlrLVWZuKXez0uK3j6Kca09saPFGh9eiqvOOkgV2AWPNl4meRG7U-dQD81FI~ydIiLMJhAugBUA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302088,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302088/thumbnails/1.jpg","file_name":"1605.02705v2.pdf","download_url":"https://www.academia.edu/attachments/82302088/download_file","bulk_download_file_name":"Integration_over_the_quantum_diagonal_su.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302088/1605.02705v2-libre.pdf?1647582026=\u0026response-content-disposition=attachment%3B+filename%3DIntegration_over_the_quantum_diagonal_su.pdf\u0026Expires=1733907351\u0026Signature=XbWtuE~fnK38mzeMV1iUhD2HE0S8rbMrtMavcC~NetsXDs3-Wcvs9vWtiW7VopRKeyU7K-h5FNSKZ44vrDQTOFMThxJYaRoZK0VJVuMS~2xRAZy3Oaew8PyWtoUl16R57so5EOI3TySpOPmu2ai15UTAkjhox6GnUE8M4QE7IR3GWrs8OnMVDRhKCBHzOApZuLFzIU737gMIoooQ9FeNClB4dy7eZxoDsO0rxn775EwlpB~apNJbQCsfPBtj8ypKKtuvRLmnzFx9dyPtlPDo0wSz0PkRxmPL-pBjpkhd9g~HummzBEuLgxLqTf8ht-IkA9~0HC0Bv3JJWEXulz260Q__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589293,"url":"https://arxiv.org/pdf/1605.02705v2.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982378"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal"><img alt="Research paper thumbnail of Weak amenability of Fourier algebras and local synthesis of the anti-diagonal" class="work-thumbnail" src="https://attachments.academia-assets.com/82302086/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal">Weak amenability of Fourier algebras and local synthesis of the anti-diagonal</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G i...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="58652a07ef7087b385d38a1fa9a10a0b" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302086,"asset_id":73982378,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302086/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982378"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982378"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982378; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982378]").text(description); $(".js-view-count[data-work-id=73982378]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982378; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982378']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982378, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "58652a07ef7087b385d38a1fa9a10a0b" } } $('.js-work-strip[data-work-id=73982378]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982378,"title":"Weak amenability of Fourier algebras and local synthesis of the anti-diagonal","translated_title":"","metadata":{"abstract":"We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.","publication_date":{"day":18,"month":2,"year":2015,"errors":{}}},"translated_abstract":"We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.","internal_url":"https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal","translated_internal_url":"","created_at":"2022-03-17T21:40:36.446-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":82302086,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302086/thumbnails/1.jpg","file_name":"1502.05214v1.pdf","download_url":"https://www.academia.edu/attachments/82302086/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Weak_amenability_of_Fourier_algebras_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302086/1502.05214v1-libre.pdf?1647582025=\u0026response-content-disposition=attachment%3B+filename%3DWeak_amenability_of_Fourier_algebras_and.pdf\u0026Expires=1733907351\u0026Signature=L1L5vV-L-u~zRl3voyv3Qlgf9L5tbj18LdZwMOaQok835zGHzKcoWRqk4QnLc0bWmW~8saREWouRJHmLtj5GNvNM2GQmg8j46GZ0VZqI-nLbABMpWs7FWE17-BenmOM-uCVVG8vDvbtq1sLAMlAddESJ0IKt9OPxiMa3GPsBuaHvQ26dgpwpq-VW~membj8DdBaUw4IYLpOc7jzl0DxTmYJs3sFxvmrPa8omCo-MFwyBNRFJ-GFP9gz1ptqgIXqxqoiGUnzcxr0epiGnluqP9KYiAh4~p51NXxH59Dj1uDCCQI0AUUt27C4UFXO7731pn994VQ5XSO7FB6riDO3oKA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal","translated_slug":"","page_count":24,"language":"en","content_type":"Work","summary":"We show that for a connected Lie group G, its Fourier algebra A(G) is weakly amenable only if G is abelian. Our main new idea is to show that weak amenability of A(G) implies that the anti-diagonal, Δ̌_G={(g,g^-1):g∈ G}, is a set of local synthesis for A(G× G). We then show that this cannot happen if G is non-abelian. We conclude for a locally compact group G, that A(G) can be weakly amenable only if it contains no closed connected non-abelian Lie subgroups. In particular, for a Lie group G, A(G) is weakly amenable if and only if its connected component of the identity G_e is abelian.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302086,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302086/thumbnails/1.jpg","file_name":"1502.05214v1.pdf","download_url":"https://www.academia.edu/attachments/82302086/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Weak_amenability_of_Fourier_algebras_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302086/1502.05214v1-libre.pdf?1647582025=\u0026response-content-disposition=attachment%3B+filename%3DWeak_amenability_of_Fourier_algebras_and.pdf\u0026Expires=1733907351\u0026Signature=L1L5vV-L-u~zRl3voyv3Qlgf9L5tbj18LdZwMOaQok835zGHzKcoWRqk4QnLc0bWmW~8saREWouRJHmLtj5GNvNM2GQmg8j46GZ0VZqI-nLbABMpWs7FWE17-BenmOM-uCVVG8vDvbtq1sLAMlAddESJ0IKt9OPxiMa3GPsBuaHvQ26dgpwpq-VW~membj8DdBaUw4IYLpOc7jzl0DxTmYJs3sFxvmrPa8omCo-MFwyBNRFJ-GFP9gz1ptqgIXqxqoiGUnzcxr0epiGnluqP9KYiAh4~p51NXxH59Dj1uDCCQI0AUUt27C4UFXO7731pn994VQ5XSO7FB6riDO3oKA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":82302085,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302085/thumbnails/1.jpg","file_name":"1502.05214v1.pdf","download_url":"https://www.academia.edu/attachments/82302085/download_file","bulk_download_file_name":"Weak_amenability_of_Fourier_algebras_and.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302085/1502.05214v1-libre.pdf?1647582024=\u0026response-content-disposition=attachment%3B+filename%3DWeak_amenability_of_Fourier_algebras_and.pdf\u0026Expires=1733907351\u0026Signature=XHS5EhlV6pK6Ot9xvwb8qApNE07TgX1gGuqmjd9uzJ9WEz-RBxLMhZcxXBRLibiUZNhEeJzLdihXKWqwXbuDJLq4eN-FNqmUtnWJuAmVDA5GiUR2dXJuvUhWo3jns917YPKmMi4pMKys9r0xasNmLt9TLdxgg0AHihG5FfFWOzkK5D4SwoZV0uZcuP2ja~ULLZmAOzYz5HpcrXjHWoqu~nkXrHKR3Gfqfdy2Q2Z1NAe3xeUYJULHhf27CBBkJC2BJaJyMblB4cSuB2SpR0ND7bzsj66OJ9K6PqXPflDEE80cmVLfJPGrUWG67DR2v9ErON0YU6xwT3WPE8TincSNwg__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[{"id":18589291,"url":"https://arxiv.org/pdf/1502.05214v1.pdf"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982375"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982375/Quantum_channels_with_quantum_group_symmetry"><img alt="Research paper thumbnail of Quantum channels with quantum group symmetry" class="work-thumbnail" src="https://attachments.academia-assets.com/82302083/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982375/Quantum_channels_with_quantum_group_symmetry">Quantum channels with quantum group symmetry</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups f...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion rule, which provides a wide generalization of some recent results. The presence of quantum group symmetry contrast to the group symmetry will be highlighted in the examples of quantum permutation groups and SU_q(2). In the latter example, we will see the necessity of the Heisenberg picture coming from the non-Kac type condition. This paper ends with the covariance with respect to projective representations, which leads us back to Weyl covariant channels and its fermionic analogue.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="08b40bd78c03b3e7ddb0be513a424610" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302083,"asset_id":73982375,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302083/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982375"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982375"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982375; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982375]").text(description); $(".js-view-count[data-work-id=73982375]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982375; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982375']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982375, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "08b40bd78c03b3e7ddb0be513a424610" } } $('.js-work-strip[data-work-id=73982375]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982375,"title":"Quantum channels with quantum group symmetry","translated_title":"","metadata":{"abstract":"In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982371"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982371/Quantum_Channels_with_Quantum_Group_Symmetry"><img alt="Research paper thumbnail of Quantum Channels with Quantum Group Symmetry" class="work-thumbnail" src="https://attachments.academia-assets.com/82302160/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982371/Quantum_Channels_with_Quantum_Group_Symmetry">Quantum Channels with Quantum Group Symmetry</a></div><div class="wp-workCard_item"><span>Communications in Mathematical Physics</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups f...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. We, then, unearth the structure of the convex set of covariant channels by identifying all extreme points under the assumption of multiplicity-free condition for the associated fusion rule, which provides a wide generalization of the results of [MSD17]. The presence of quantum group symmetry contrast to the group symmetry will be highlighted in the examples of quantum permutation groups and SU q (2). In the latter example, we will see the necessity of the Heisenberg picture coming from the non-Kac type condition. This paper ends with the covariance with respect to projective representations, which leads us back to Weyl covariant channels and its fermionic analogue.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="6383898acbfe280c5470ed24aa4d9003" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302160,"asset_id":73982371,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302160/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982371"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982371"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982371; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982371]").text(description); $(".js-view-count[data-work-id=73982371]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982371; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982371']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982371, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "6383898acbfe280c5470ed24aa4d9003" } } $('.js-work-strip[data-work-id=73982371]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982371,"title":"Quantum Channels with Quantum Group Symmetry","translated_title":"","metadata":{"publisher":"Springer Science and Business Media LLC","grobid_abstract":"In this paper we will demonstrate that any compact quantum group can be used as symmetry groups for quantum channels, which leads us to the concept of covariant channels. 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Two-dimensional restricted lattices admitting the Kronecker product structure are listed, and their spectral distributions are calculated in terms of elliptic integrals.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="211040cb6e7330b77b7132811595a6c6" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302079,"asset_id":73982369,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302079/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982369"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982369"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982369; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982369]").text(description); $(".js-view-count[data-work-id=73982369]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982369; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982369']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982369, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "211040cb6e7330b77b7132811595a6c6" } } $('.js-work-strip[data-work-id=73982369]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982369,"title":"Kronecker Product Graphs and Counting Walks in Restricted Lattices","translated_title":"","metadata":{"abstract":"Formulas are derived for counting walks in the Kronecker product of graphs, and the associated spectral distributions are obtained by the Mellin convolution of probability distributions. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982367"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982367/Similarity_degree_of_Fourier_algebras"><img alt="Research paper thumbnail of Similarity degree of Fourier algebras" class="work-thumbnail" src="https://attachments.academia-assets.com/82302159/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982367/Similarity_degree_of_Fourier_algebras">Similarity degree of Fourier algebras</a></div><div class="wp-workCard_item"><span>Journal of Functional Analysis</span><span>, 2016</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We show that for a locally compact group G, amongst a class which contains amenable and small inv...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier's similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π : A(G) → B(H) admits an invertible S in B(H) for which S S −1 ≤ π 2 cb and S −1 π(•)S extends to a *-representation of the C*-algebra C 0 (G). This significantly improves some results due to Brannan and Samei (</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="4d8315dd894ef360405b860daca29355" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":82302159,"asset_id":73982367,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/82302159/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982367"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982367"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982367; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982367]").text(description); $(".js-view-count[data-work-id=73982367]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982367; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982367']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982367, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "4d8315dd894ef360405b860daca29355" } } $('.js-work-strip[data-work-id=73982367]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982367,"title":"Similarity degree of Fourier algebras","translated_title":"","metadata":{"publisher":"Elsevier BV","grobid_abstract":"We show that for a locally compact group G, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra A(G) satisfies a completely bounded version Pisier's similarity property with similarity degree at most 2. Specifically, any completely bounded homomorphism π : A(G) → B(H) admits an invertible S in B(H) for which S S −1 ≤ π 2 cb and S −1 π(•)S extends to a *-representation of the C*-algebra C 0 (G). 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Specifically, any completely bounded homomorphism π : A(G) → B(H) admits an invertible S in B(H) for which S S −1 ≤ π 2 cb and S −1 π(•)S extends to a *-representation of the C*-algebra C 0 (G). This significantly improves some results due to Brannan and Samei (","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":82302159,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/82302159/thumbnails/1.jpg","file_name":"1511.pdf","download_url":"https://www.academia.edu/attachments/82302159/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Similarity_degree_of_Fourier_algebras.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/82302159/1511-libre.pdf?1647582018=\u0026response-content-disposition=attachment%3B+filename%3DSimilarity_degree_of_Fourier_algebras.pdf\u0026Expires=1733907351\u0026Signature=PCMs2b8w4X~CTpg84xSaLBCGSF2EhGeaiyFggPA7GLHuWp3T2hkMwde2mQ0UD5BG6L-1UmupKyVYmQsgYHamFtPPaaWPJwKgwkwWoIWkEexjpI7foc2daIlB5MAViewyhhulpD4JQ1WCMvwO7f2OU~B-n64Di9sezTth9gRcdIGSbeemzTG4JwDM3g-PdGjsb8bMJniA8X14w1hKaCvl9Cfmciap4u3uRVGATmAiqAD2z3F1DT1S1kIlSj95y6tp~rhKUQSMayK6tZnOl4e81gL1aSDV-89~pvvpAcEVgfh1zZZA2SEy8aIxb3UnEeMDZk5Q6W83co0V-yL2u-YXCQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":300,"name":"Mathematics","url":"https://www.academia.edu/Documents/in/Mathematics"},{"id":371,"name":"Functional Analysis","url":"https://www.academia.edu/Documents/in/Functional_Analysis"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="73982366"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/73982366/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups"><img alt="Research paper thumbnail of New deformations of Convolution algebras and Fourier algebras on locally compact groups" class="work-thumbnail" src="https://attachments.academia-assets.com/83819308/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/73982366/New_deformations_of_Convolution_algebras_and_Fourier_algebras_on_locally_compact_groups">New deformations of Convolution algebras and Fourier algebras on locally compact groups</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on lo...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some informations of the underlying groups by examinining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similary, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="e1e5f96c180798695024b55339fd927c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83819308,"asset_id":73982366,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83819308/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982366"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982366"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982366; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982366]").text(description); $(".js-view-count[data-work-id=73982366]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982366; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982366']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982366, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "e1e5f96c180798695024b55339fd927c" } } $('.js-work-strip[data-work-id=73982366]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982366,"title":"New deformations of Convolution algebras and Fourier algebras on locally compact groups","translated_title":"","metadata":{"grobid_abstract":"In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. 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We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 &lt;α&lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="274bcf7d6803c303accdf4b46b771077" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":83819313,"asset_id":73982365,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/83819313/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="73982365"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="73982365"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 73982365; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=73982365]").text(description); $(".js-view-count[data-work-id=73982365]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 73982365; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='73982365']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 73982365, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "274bcf7d6803c303accdf4b46b771077" } } $('.js-work-strip[data-work-id=73982365]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":73982365,"title":"Some Weighted Group Algebras are Operator Algebras","translated_title":"","metadata":{"abstract":"LetGbe a finitely generated group with polynomial growth, and letωbe a weight, i.e. a sub-multiplicative function onGwith positive values. We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 \u0026lt;α\u0026lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.","publisher":"Cambridge University Press (CUP)","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Proceedings of the Edinburgh Mathematical Society"},"translated_abstract":"LetGbe a finitely generated group with polynomial growth, and letωbe a weight, i.e. a sub-multiplicative function onGwith positive values. We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 \u0026lt;α\u0026lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.","internal_url":"https://www.academia.edu/73982365/Some_Weighted_Group_Algebras_are_Operator_Algebras","translated_internal_url":"","created_at":"2022-03-17T21:40:35.008-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":13534588,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":83819313,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/83819313/thumbnails/1.jpg","file_name":"Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf","download_url":"https://www.academia.edu/attachments/83819313/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Weighted_Group_Algebras_are_Operato.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/83819313/Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf?1649706689=\u0026response-content-disposition=attachment%3B+filename%3DSome_Weighted_Group_Algebras_are_Operato.pdf\u0026Expires=1733907351\u0026Signature=ExKXoQuKMgJ3q3YBGEEsStXr3UbhAySxvb9pIAPsxi7rtTqDPx2ejiYLEzRHLsrYYpk2DwSOLG94Xm8Lrl~B5ftsPFxTBywEshvKUak4t0BE4AB-wtOnk0NAaJjuQCO5TImKJx8DXYwvnaikBiHeB5Z~QzsmeaCDOkcp982BoZD82ZQPFBAg1C1jIq2Zfz-nz8-6EkZj9uybRKv-vrs3DpiMmXnjM7HAgcZKrq7QDIRujLDpLDoP4kB-z7qOCdKR4oLixQ~~Pemk4gDqCIddO95o8VBWvPuL8x0CdpJrUNu-4Qq12eNMac15uKsTgYDwWPxqC8nVpZC3A0OfTQSmGw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Some_Weighted_Group_Algebras_are_Operator_Algebras","translated_slug":"","page_count":19,"language":"en","content_type":"Work","summary":"LetGbe a finitely generated group with polynomial growth, and letωbe a weight, i.e. a sub-multiplicative function onGwith positive values. We study when the weighted group algebraℓ1(G, ω) is isomorphic to an operator algebra. We show thatℓ1(G, ω) is isomorphic to an operator algebra ifωis a polynomial weight with large enough degree or an exponential weight of order 0 \u0026lt;α\u0026lt; 1. We demonstrate that the order of growth ofGplays an important role in this problem. Moreover, the algebraic centre ofℓ1(G, ω) is isomorphic to aQ-algebra, and hence satisfies a multi-variable von Neumann inequality. We also present a more detailed study of our results whenGconsists of thed-dimensional integers ℤdor the three-dimensional discrete Heisenberg group ℍ3(ℤ). The case of the free group with two generators is considered as a counter-example of groups with exponential growth.","owner":{"id":13534588,"first_name":"Hun Hee","middle_initials":null,"last_name":"Lee","page_name":"HunHeeLee","domain_name":"independent","created_at":"2014-07-03T01:55:32.695-07:00","display_name":"Hun Hee Lee","url":"https://independent.academia.edu/HunHeeLee"},"attachments":[{"id":83819313,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/83819313/thumbnails/1.jpg","file_name":"Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf","download_url":"https://www.academia.edu/attachments/83819313/download_file?st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&st=MTczMzkwMzc1MSw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Some_Weighted_Group_Algebras_are_Operato.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/83819313/Some_Weighted_Group_Algebras_are_Operato20220411-1-osk9iv.pdf?1649706689=\u0026response-content-disposition=attachment%3B+filename%3DSome_Weighted_Group_Algebras_are_Operato.pdf\u0026Expires=1733907351\u0026Signature=ExKXoQuKMgJ3q3YBGEEsStXr3UbhAySxvb9pIAPsxi7rtTqDPx2ejiYLEzRHLsrYYpk2DwSOLG94Xm8Lrl~B5ftsPFxTBywEshvKUak4t0BE4AB-wtOnk0NAaJjuQCO5TImKJx8DXYwvnaikBiHeB5Z~QzsmeaCDOkcp982BoZD82ZQPFBAg1C1jIq2Zfz-nz8-6EkZj9uybRKv-vrs3DpiMmXnjM7HAgcZKrq7QDIRujLDpLDoP4kB-z7qOCdKR4oLixQ~~Pemk4gDqCIddO95o8VBWvPuL8x0CdpJrUNu-4Qq12eNMac15uKsTgYDwWPxqC8nVpZC3A0OfTQSmGw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":19997,"name":"Pure Mathematics","url":"https://www.academia.edu/Documents/in/Pure_Mathematics"}],"urls":[]}, dispatcherData: dispatcherData }); 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