A matrix formulation of Grüss inequality
type: Item
instance of: scholarly article
title: A matrix formulation of Grüss inequality
zbMATH Open document ID: 0982.15025
DOI: 10.1016/S0024-3795(01)00278-6
author: Peter F. Renaud
published in: Linear Algebra and its Applications
publication date: 2002-04-02T00:00:00Z
reviewed by: Ki Hang Kim
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 47A12
zbMATH DE Number: 1661140
zbMATH Keywords: Grüss inequality
zbMATH Keywords: trace inequality
zbMATH Keywords: Hilbert space
zbMATH Keywords: numerical ranges
MaRDI profile type: Publication
cites work: Q3146526
cites work: Q3873024
review text: The main result of this paper is Theorem 3.1: If \(A,B\) are bounded linear operations on a Hilbert space and their numerical ranges are contained in disks of radii \(R\) and \(S\) respectively, and \(T\) is a trace operator, then NEWLINE\[NEWLINE|Tr (TAB) -Tr (TA) Tr (TB) |\leq 4RSNEWLINE\]NEWLINE If \(A,B\) are normal, the \(4\) can be replaced by \(1\). This implies other well-known inequalities.
description: scientific article; zbMATH DE number 1661140