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2013 Matrix inequalities related to Hölder inequality
Hussien Albadawi
Banach J. Math. Anal. 7(2): 162-171 (2013). DOI: 10.15352/bjma/1363784229

Abstract

Matrix inequalities of Hölder type are obtained. Among other inequalities, it is shown that if $p,q \in (2,\infty) $ and $r>1$ with $1/p+1/q=1-1/r$, then for any $A_{i},B_{i}\in M_{n}\left(\mathbb{C} \right) $ and $\alpha _{i}\in \left[ 0,1\right] $ $\left( i=1,2,\cdots ,m\right) $ with $\sum\limits_{i=1}^{m}\alpha _{i}=1$, we have% \begin{equation*} \left\vert \sum\limits_{i=1}^{m}\alpha _{i}^{1/r}B_{i}A_{i}\right\vert \leq \left( \sum\limits_{i=1}^{m}\left\vert A_{i}\right\vert ^{p}\right) ^{1/p} \end{equation*}% whenever $\sum\limits_{i=1}^{m}\left\vert B_{i}^{\ast }\right\vert ^{q}\leq I $. Related unitarily invariant norm inequalities are also presented.

Citation

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Hussien Albadawi . "Matrix inequalities related to Hölder inequality." Banach J. Math. Anal. 7 (2) 162 - 171, 2013. https://doi.org/10.15352/bjma/1363784229

Information

Published: 2013
First available in Project Euclid: 20 March 2013

zbMATH: 1270.15012
MathSciNet: MR3039945
Digital Object Identifier: 10.15352/bjma/1363784229

Subjects:
Primary: 15A45
Secondary: 15A60, 15B48, 47A30

Rights: Copyright © 2013 Tusi Mathematical Research Group

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Vol.7 • No. 2 • 2013
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