Comparison of various means for operators
type: Item
instance of: scholarly article
title: Comparison of various means for operators
zbMATH Open document ID: 0929.47009
author: Hideki Kosaki
author: Fumio Hiai
published in: Journal of Functional Analysis
publication date: 2000-01-25T00:00:00Z
review text: Let \(A\), \(B\) be nonnegative Hilbert space operators and let \(T\) be an arbitrary linear bounded operator, all acting on a Hilbert space. The inequality \[ \| A^{1/2} TB^{1/2}\|\leq 1/2\| AT+ TB\|, \] was only recently found in operator theory, in connection with some concrete problems of harmonic analysis, see \textit{R. Bhatia} and \textit{C. Davis} [SIAM J. Matrix Annal. Appl. 14, 132-136 (1993; Zbl 0767.15012)]. The note under review contains several interesting refinements and generalizations of this inequality.
reviewed by: Mihai Putinar
Mathematics Subject Classification ID: 47A63
zbMATH DE Number: 1286370
zbMATH Keywords: geometric mean
zbMATH Keywords: arithmetic mean
MaRDI profile type: Publication
full work available at URL: jfan.1998.3375
OpenAlex ID: W2003935125
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DOI: 10.1006/JFAN.1998.3375
description: scientific article; zbMATH DE number 1286370