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            <title xml:lang="en">Some norm inequalities for some positive block matrices</title>
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            <idno type="halRefHtml">&lt;i&gt;Miskolc Mathematical Notes&lt;/i&gt;, 2023, 24 (1), pp.301-308. &lt;a target="_blank" href="https://dx.doi.org/10.18514/MMN.2023.3801"&gt;&amp;#x27E8;10.18514/MMN.2023.3801&amp;#x27E9;&lt;/a&gt;</idno>
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                <title xml:lang="en">Some norm inequalities for some positive block matrices</title>
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                    <forename type="first">Antoine</forename>
                    <surname>Mhanna</surname>
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                <title level="j">Miskolc Mathematical Notes</title>
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                  <publisher>Miskolci Egyetemi Kiadó</publisher>
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                <term xml:lang="en">symmetric norm</term>
                <term xml:lang="en">permutations. 2010 MSC: 15A60</term>
                <term xml:lang="en">15A42</term>
                <term xml:lang="en">15B99</term>
                <term xml:lang="en">05A18</term>
                <term xml:lang="en">partial transpose</term>
                <term xml:lang="en">positive block matrix</term>
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              <p>We review Lin's inequality of numerical range widths  and prove that, if $M=[X_{i,j}]_{i,j=1}^n$  is positive semi-definite then $\bigoplus_{i=1}^{n}(X_{i,i}-\sum\limits_{j\neq i}X_{j,j})\le M^\tau \le    I_n \otimes \sum\limits_{i=1}^nX_{i,i}$, where $M^{\tau}$ is the partial transpose of $M$.  Some classical results are also discussed in terms of permutations.</p>
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