Accretive operators and Cassels inequality
type: Item
instance of: scholarly article
title: Accretive operators and Cassels inequality
zbMATH Open document ID: 1193.15018
author: M. Niezgoda
published in: Linear Algebra and its Applications
publication date: 2010-05-21T00:00:00Z
review text: Based on the notion of accretive operator, the author presents a method of extending the range of applicability of some matrix inequalities. He extends some inequalities from positive definite matrices to the case of matrices \(Z\) having an accretive transform \((Z-mI)^{\ast }(MI-Z)\). One of the results is the following: Let \(A,Z\in M_{n}(R)\) with \(A\geq 0\) and let scalars \(m,M\) be positive such that \(\text{Re}\langle h,(Z-mI)^{\ast }(MI-Z)h\rangle \geq 0\) for all \(h\in R^n\). Then \[ Tr~|AZ| \leq \frac{M+m}{2\sqrt{Mm}}Tr~AZ, \] where \(|U|=(U^{\ast }U)^{1/2}\).
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5710779
zbMATH Keywords: accretive operator
zbMATH Keywords: Cassel inequality
zbMATH Keywords: positive linear map
zbMATH Keywords: geometric means of matrices
zbMATH Keywords: eigenvalues
zbMATH Keywords: singular values
zbMATH Keywords: unitarily invariant norm
zbMATH Keywords: trace
zbMATH Keywords: positive definite matrices
reviewed by: Fozi Dannan
MaRDI profile type: Publication
full work available at URL: j.laa.2010.01.038
OpenAlex ID: W1995438677
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DOI: 10.1016/J.LAA.2010.01.038
description: scientific article; zbMATH DE number 5710779