A Cauchy-Schwarz inequality for operators with applications

Bhatia, Rajendra ; Davis, Chandler (1995) A Cauchy-Schwarz inequality for operators with applications Linear Algebra and its Applications, 223-224 . pp. 119-129. ISSN 0024-3795

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Official URL: http://dx.doi.org//10.1016/0024-3795(94)00344-D

Related URL: http://dx.doi.org/10.1016/0024-3795(94)00344-D

Abstract

For any unitarily invariant norm on Hilbert-space operators it is shown that for all operators A, B, X and positive real numbers r we have ||| |AXB|r |||2 ||| |AAX|r ||| ||| |XBB|r |||. Some consequences are then discussed. A simple proof is given for the fact that for positive operators A, B the function [spr(AtBt)]1/t is monotone in t on the positive half line.

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