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arXiv · 1109.1778

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

Cristian Conde·Mohammad Sal Moslehian·Ameur Seddik
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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.

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Cristian Conde, Mohammad Sal Moslehian, Ameur Seddik. 2011-09-08. Operator inequalities related to the Corach--Porta--Recht inequality. https://arxiv.org/abs/1109.1778

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