Garske's inequality for an \(n\)-tuple of operators
type: Item
instance of: scholarly article
title: Garske's inequality for an \(n\)-tuple of operators
zbMATH Open document ID: 0802.47006
DOI: 10.1007/BF01198937
author: Fan Ming
published in: Integral Equations and Operator Theory
publication date: 1992-09-27T00:00:00Z
review text: For an arbitrary bounded linear operator \(T\) on a Hilbert space Garske's inequality \[ \sup_{\| x\|=1}\{\| Tx\|^ 2- |(Tx,x)|^ 2\}\geq R^ 2_ T\tag{1} \] is true. Here \(R_ T\) is the radius of the smallest disc containing the spectrum of \(\Gamma\). In the paper the following generalization of (1) is proved: Any \(n\)-tuple of commuting operators \(T=(T_ 1,T_ 2,\ldots,T_ n)\) satisfies the inequality (1), where \(R_ T\) is the radius of the smallest ball containing the Taylor spectrum of \(\Gamma\).
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 47A13
zbMATH DE Number: 59721
zbMATH Keywords: Garske's inequality
zbMATH Keywords: Taylor spectrum
zbMATH Keywords: commuting operators
reviewed by: Lev A. Sakhnovich
MaRDI profile type: Publication
cites work: Approximate Proper Vectors
cites work: Some classes of commuting n-tuples of operators
cites work: Q3203570
cites work: An Inequality Concerning the Smallest Disc that Contains the Spectrum of an Operator
cites work: The analytic-functional calculus for several commuting operators
cites work: The boundary of Taylor's joint spectrum for two commuting Banach space operators
cites work: Joint spectra and joint numerical ranges for pairwise commuting operators in Banach spaces
full work available at URL: https://doi.org/10.1007/bf01198937
OpenAlex ID: W2976209
Recommended article: Inequalities for \(N\)-operator
Recommended article: Q3194020
Recommended article: On Clarkson-McCarthy inequalities for $n$-tuples of operators
Recommended article: Khinchin's inequality for operators
Recommended article: A trace inequality for commuting \(d\)-tuples of operators
Recommended article: Non-commutative Clarkson inequalities for \(n\)-tuples of operators
Recommended article: An operator Karamata inequality
Recommended article: Operator versions of the Kantorovich inequality
Recommended article: An operator inequality related to Jensen's inequality
Recommended article: ON AN OPERATORIAL INEQUALITY
description: scientific article; zbMATH DE number 59721