Document Zbl 1542.47013

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Funct. Anal. Optim.</a> <a href="/?q=in%3A501257" title="Articles in this Issue">44, No. 11, 1097-1118 (2023)</a>. </div> <div class="abstract">Summary: Our aim in this article is to establish several new norm and numerical radius inequalities for products and sums of operators acting on a complex Hilbert space $(\mathcal{H}, \langle \cdot, \cdot\rangle)$. Some of the obtained inequalities improve well-known ones. In addition, by using new techniques, we prove certain new inequalities related to $\omega_A(\cdot)$ and $\| \cdot \|_A$, where $\omega_A(T)$ and $\|T\|_A$ denote the $A$-numerical radius and the $A$-operator seminorm of an operator $T$ acting on the semi-Hilbert space $(\mathcal{H}, \langle \cdot, \cdot\rangle_A)$ respectively. Here $\langle x, y\rangle_A := \langle Ax, y\rangle$ for every $x, y \in \mathcal{H}$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7729083">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><tr> <td> <a class="mono" href="/classification/?q=cc%3A47B02" title="MSC2020">47B02</a> </td> <td class="space"> Operators on Hilbert spaces (general) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Anumerical+radius">numerical radius</a>; <a href="/?q=ut%3Apositive+operator">positive operator</a>; <a href="/?q=ut%3Aproduct">product</a>; <a href="/?q=ut%3Aseminorm">seminorm</a>; <a href="/?q=ut%3Asemi-inner+product">semi-inner product</a>; <a href="/?q=ut%3Asum">sum</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 1542.47013" data-ciurl="/ci/07729083" data-biburl="/bibtex/07729083.bib" data-amsurl="/amsrefs/07729083.bib" data-xmlurl="/xml/07729083.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07729083.pdf" title="Zbl 1542.47013 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/10.1080/01630563.2023.2221897" aria-label="DOI for “Further seminorm and numerical radius inequalities for products and sums of operators”" title="10.1080/01630563.2023.2221897">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Bhunia, P.; Paul, K., Refinements of norm and numerical radius inequalities, Rocky Mountain J. 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