http://openproblemgarden.org/op/trace_inequality Comments for "trace inequality" en http://openproblemgarden.org/op/trace_inequality#comment-6881 <p>this inequality is not true. It was denied some years ago. See X.Z Zhan's <matrix inequalities></p> Sun, 19 Dec 2010 23:47:20 +0100 Anonymous comment 6881 at http://openproblemgarden.org http://openproblemgarden.org/op/trace_inequality#comment-6787 <p>I suppose that A and B are square hermitian matrixes and that s and r are real numbers. But what are the brackets supposed to represent? Sorry for my ignorance if it is obvious.</p> Sat, 28 Aug 2010 14:25:26 +0200 ojs comment 6787 at http://openproblemgarden.org http://openproblemgarden.org/op/trace_inequality#comment-2427 <p>It is open.</p> Sun, 12 Oct 2008 11:42:49 +0200 Miwa Lin comment 2427 at http://openproblemgarden.org http://openproblemgarden.org/op/trace_inequality <table cellspacing="10"> <tr> <td> Author(s): <a href="/kpz_equation_central_limit_theorem"></a>&nbsp;&nbsp; </td> <td align=right> Subject: <a href="/category/algebra">Algebra</a>&nbsp;&nbsp; </td> </tr> <tr> <td colspan=2> <table border=1 cellspacing="5"> <tr><td> <p>Let <img class="teximage" src="/files/tex/1b13f4b9d66832f9a590af8be2dcc18a2c147d4f.png" alt="$ A,B $" /> be positive semidefinite, by Jensen's inequality, it is easy to see <img class="teximage" src="/files/tex/f5fa90ccf8c1dde9b9bf1f21399b3b5428dab81d.png" alt="$ [tr(A^s+B^s)]^{\frac{1}{s}}\leq [tr(A^r+B^r)]^{\frac{1}{r}} $" />, whenever <img class="teximage" src="/files/tex/437bd3564709db19f774bc100776e7b17b7f0381.png" alt="$ s&gt;r&gt;0 $" />.</p> <p>What about the <img class="teximage" src="/files/tex/e74dfa72ae7f138c9a2ed8cf80507bfbeb1b3004.png" alt="$ tr(A^s+B^s)^{\frac{1}{s}}\leq tr(A^r+B^r)^{\frac{1}{r}} $" />, is it still valid?</p> </tr></td> </table> </td> </tr> </table> Algebra http://openproblemgarden.org/op/trace_inequality#comment Sat, 11 Oct 2008 15:03:55 +0200 Miwa Lin 3031 at http://openproblemgarden.org