On some operator norm inequalities
type: Item
instance of: scholarly article
title: On some operator norm inequalities
zbMATH Open document ID: 1061.47011
author: Ameur Seddik
published in: Linear Algebra and its Applications
publication date: 2004-11-22T00:00:00Z
review text: Let \(B(H)\) be the \(C^{*}\)-algebra of all bounded linear operators on a complex Hilbert space \(H\), and let \((I, \| \cdot\| _{I})\) denote a norm ideal of \(B(H)\). For \(A, B\in B(H)\), the author defines the two operators \(U_{I,A,B}(X)=AXB+BXA\) and \(V_{I,A,B}(X)=AXB-BXA\) on \(I\). Then the author obtains lower and upper bounds of \(U_{I,S,S^{-1}}\) and \(V_{I,S,S^{-1}}\) in the case that \(S\) is an invertible and self-adjoint operator. Using this result, the author obtains the following norm inequality: \[ \| SXS^{-1}-S^{-1}XS\| _{I} \leq (\| S\| \| S^{-1}\| -1) \| SXS^{-1}+S^{-1}XS\| _{I} \] for \(X\in I\) and \(S=S^{*}\). This is another type of the inequality shown in [\textit{F. Kittaneh}, Linear Algebra Appl. 208--209, 19--28 (1994; Zbl 0803.47019)].
reviewed by: Takeaki Yamazaki
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47B10
zbMATH DE Number: 2117291
zbMATH Keywords: Hilbert space
zbMATH Keywords: norm ideal
zbMATH Keywords: operator norm inequality
zbMATH Keywords: self-adjoint operator
MaRDI profile type: Publication
full work available at URL: j.laa.2004.03.027
OpenAlex ID: W2073434959
cites work: An operator inequality
cites work: On some operator inequalities
cites work: On the Numerical Range and Norm of Elementary Operators
cites work: Some results related to the Corach-Porta-Recht inequality
DOI: 10.1016/J.LAA.2004.03.027
description: scientific article; zbMATH DE number 2117291