Operator inequalities related to the Corach--Porta--Recht inequality

Cristian Conde; Mohammad Sal Moslehian; Ameur Seddik

Operator inequalities related to the Corach--Porta--Recht inequality

Functional Analysis 2012-03-21 v1

Authors: Cristian Conde , Mohammad Sal Moslehian , Ameur Seddik

Abstract

We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach--Porta--Recht inequality. We also characterize the class of operators satisfying $\left\Vert SXS^{-1}+S^{-1}XS+kX\right\Vert \geq (k+2)\left\Vert X\right\Vert$ under certain conditions.

Keywords

operator inequality Corach–Porta–Recht inequality Heinz inequality complex Hilbert space refinement operator norm

Cite

@article{arxiv.1109.1778,
  title  = {Operator inequalities related to the Corach--Porta--Recht inequality},
  author = {Cristian Conde and Mohammad Sal Moslehian and Ameur Seddik},
  journal= {arXiv preprint arXiv:1109.1778},
  year   = {2012}
}

Comments

12 Pages, to appear in Linear Algebra Appl. (LAA)

Operator inequalities related to the Corach--Porta--Recht inequality

Abstract

Keywords

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