Some numerical radius inequalities for Hilbert space operators
type: Item
instance of: scholarly article
title: Some numerical radius inequalities for Hilbert space operators
zbMATH Open document ID: 1185.47004
author: Mohsen Erfanian Omidvar
author: Mohammad Sal Moslehian
author: Assadollah Niknam
published in: Involve
publication date: 2010-02-23T00:00:00Z
review text: Let \(B(H)\) denote the \(C^*\) algebra of all bounded operators on a complex Hilbert space \(H\) with inner product \(\langle\cdot,\cdot\rangle\). The authors treat numerical radius and related inequalities in the present paper. Their main result says that, if \(A,B,C,D \in B(H)\) and \(T = \left[\begin{smallmatrix} A &B\\ C &D \end{smallmatrix}\right]\), then \(\max(w(A),w(D))\leq\frac12(\| T\| + \| T^2\|^{\frac12})\) and \(\max((w(BC)^{\frac12}, w(CB)^{\frac12})\leq\frac12(\|T\|+\|T^2\|^{\frac12})\). Moreover, they prove that, if \(A \in B(H)\) is positive, then \(w(AX-XA)\leq\frac12\|A\|(\|X\|+\|X^2\|^{\frac12})\). The authors both sharpen and provide some new proofs of previously established inequalities and they also mention some applications.
reviewed by: V. Lokesha
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 46C15
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5673995
zbMATH Keywords: bounded linear operator
zbMATH Keywords: Hilbert space
zbMATH Keywords: norm inequality
zbMATH Keywords: numerical radius
zbMATH Keywords: positive operator
MaRDI profile type: Publication
full work available at URL: involve.2009.2.471
OpenAlex ID: W2144301560
DOI: 10.2140/INVOLVE.2009.2.471
description: scientific article; zbMATH DE number 5673995