Document Zbl 07354312

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Inequal. Appl.</a> <a href="/?q=in%3A463979" title="Articles in this Issue">24, No. 2, 405-420 (2021)</a>. </div> <div class="abstract">Summary: Let $\mathbf{T}=(T_1,\dots,T_d)$ be a $d$-tuple of operators on a complex Hilbert space $\mathscr{H}$. The spherical Aluthge transform of $\mathbf{T}$ is the $d$-tuple given by $\widehat{\mathbf{T}}:=(\sqrt{P}V_1\sqrt{P},\dots,\sqrt{P}V_d\sqrt{P})$ where $P:=\sqrt{T_1^\ast T_1+\dots+T_d^\ast T_d}$ and $(V_1,\dots,V_d)$ is a joint partial isometry such that $T_k=V_kP$ for all $1\leqslant k\leqslant d$. In this paper, we prove several inequalities involving the joint numerical radius and the joint operator norm of $\widehat{\mathbf{T}}$. Moreover, a characterization of the joint spectral radius of an operator tuple $\widehat{\mathbf{T}}$ via $n$-th iterated of spherical Aluthge transform is established.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7354312">Cited in <strong>12</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A13" title="MSC2020">47A13</a> </td> <td class="space"> Several-variable operator theory (spectral, Fredholm, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A12" title="MSC2020">47A12</a> </td> <td class="space"> Numerical range, numerical radius </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A47A30" title="MSC2020">47A30</a> </td> <td class="space"> Norms (inequalities, more than one norm, etc.) of linear operators </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aspherical+Aluthge+transform">spherical Aluthge transform</a>; <a href="/?q=ut%3Aduggal+transform">duggal transform</a>; <a href="/?q=ut%3Ajoint+numerical+radius">joint numerical radius</a>; <a href="/?q=ut%3Ajoint+spectral+radius">joint spectral radius</a>; <a href="/?q=ut%3Ajoint+operator+norm">joint operator norm</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 07354312" data-ciurl="/ci/07354312" data-biburl="/bibtex/07354312.bib" data-amsurl="/amsrefs/07354312.bib" data-xmlurl="/xml/07354312.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07354312.pdf" title="Zbl 07354312 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.7153/mia-2021-24-28" aria-label="DOI for “Joint numerical radius of spherical Aluthge transforms of tuples of Hilbert space operators”" title="10.7153/mia-2021-24-28">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2004.02538"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">A. 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