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The key tool in our approach is to show that the Fourier algebra of such hypergroups has the so called property (B). This property has already been shown to be very effective in solving problems related to zero product preserving maps and local derivations provided that some other conditions are satisfied. Some examples of groups and hypergroups, the Fourier algebras of which have the property (B) satisfying all those conditions are given. Our examples are the class of almost abelian groups and double coset hypergroups of Gelfand pairs. We also prove that if H is the double coset hypergroup of a Gelfand pair, then A(H) is weakly amenable. 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translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/50439780/Spectral_synthesis_in_products_and_quotients_of_hypergroups"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="73982378" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" 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 class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="13534588" href="https://independent.academia.edu/HunHeeLee">Hun Hee Lee</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2015</p><p class="ds-related-work--abstract ds2-5-body-sm">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.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Weak amenability of Fourier algebras and local synthesis of the anti-diagonal","attachmentId":82302086,"attachmentType":"pdf","work_url":"https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/73982378/Weak_amenability_of_Fourier_algebras_and_local_synthesis_of_the_anti_diagonal"><span 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href="https://www.academia.edu/92471457/Order_isomorphisms_of_Fourier_algebras">Order isomorphisms of Fourier algebras</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="229374393" href="https://independent.academia.edu/JeanDeCanni%C3%A8re">Jean De Cannière</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Functional Analysis, 1983</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Order isomorphisms of Fourier algebras","attachmentId":95471794,"attachmentType":"pdf","work_url":"https://www.academia.edu/92471457/Order_isomorphisms_of_Fourier_algebras","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free 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data-author-id="272814050" href="https://independent.academia.edu/FilaliManal">Manal Filali</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematische Annalen, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Weak factorizations of operators in the group von Neumann algebras of certain amenable groups and applications","attachmentId":103121681,"attachmentType":"pdf","work_url":"https://www.academia.edu/102998054/Weak_factorizations_of_operators_in_the_group_von_Neumann_algebras_of_certain_amenable_groups_and_applications","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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href="https://www.academia.edu/73020404/G_Hypergroups_Hypergroups_with_a_Group_Isomorphic_Heart">G-Hypergroups: Hypergroups with a Group-Isomorphic Heart</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="28038589" href="https://independent.academia.edu/MDeSalvo">Mario De Salvo</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematics</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"G-Hypergroups: Hypergroups with a Group-Isomorphic Heart","attachmentId":81708539,"attachmentType":"pdf","work_url":"https://www.academia.edu/73020404/G_Hypergroups_Hypergroups_with_a_Group_Isomorphic_Heart","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span 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href="https://colorado.academia.edu/ArlanRamsay">Arlan Ramsay</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Functional Analysis, 1997</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Fourier–Stieltjes Algebras of Locally Compact Groupoids","attachmentId":42154237,"attachmentType":"pdf","work_url":"https://www.academia.edu/21593854/Fourier_Stieltjes_Algebras_of_Locally_Compact_Groupoids","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/21593854/Fourier_Stieltjes_Algebras_of_Locally_Compact_Groupoids"><span class="ds2-5-text-link__content">View PDF</span><span 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Forrest</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Functional Analysis, 2003</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Ideals with bounded approximate identities in Fourier algebras","attachmentId":39572923,"attachmentType":"pdf","work_url":"https://www.academia.edu/17547420/Ideals_with_bounded_approximate_identities_in_Fourier_algebras","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/17547420/Ideals_with_bounded_approximate_identities_in_Fourier_algebras"><span class="ds2-5-text-link__content">View PDF</span><span 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