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arXiv · 1606.03913

A generalization of POWERS-STØRMER inequality

Anchal Aggarwal·Mandeep Singh
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Abstract

Let $A,\;B$ be the positive semidefinite matrices. A matrix version of the famous Powers-Størmer's inequality $$2Tr(A^αB^{1-α})\geq Tr(A+B-|A-B|),\;\;\;0\leqα\leq 1,$$ was proven by Audenaert et. al. We establish a comparison of eigenvalues for the matrices $A^αB^{1-α}$ and $A+B-|A-B|, \; 0 \leq α\leq 1,$ subsuming the Powers-Størmer's inequality. We also prove several related norm inequalities.

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Anchal Aggarwal, Mandeep Singh. 2016-06-13. A generalization of POWERS-STØRMER inequality. https://arxiv.org/abs/1606.03913

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