A generalization of POWERS-ST{\O}RMER inequality

Anchal Aggarwal; Mandeep Singh

A generalization of POWERS-ST{\O}RMER inequality

Functional Analysis 2016-06-14 v1 Operator Algebras

Authors: Anchal Aggarwal , Mandeep Singh

Abstract

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

Keywords

Powers-St{\o}rmer inequality positive semidefinite matrix eigenvalue comparison norm inequality matrix trace

Cite

@article{arxiv.1606.03913,
  title  = {A generalization of POWERS-ST{\O}RMER inequality},
  author = {Anchal Aggarwal and Mandeep Singh},
  journal= {arXiv preprint arXiv:1606.03913},
  year   = {2016}
}

A generalization of POWERS-ST{\O}RMER inequality

Abstract

Keywords

Cite

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