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

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

2011-09-08

arxiv.org/abs/1109.1778v1

Linear Algebra Appl. 436 (2012), no. 9, 3008-3017

Mathematics

Functional Analysis

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

Scientific paper

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.

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