Linear maps preserving invertibility or related spectral properties
type: Item
instance of: scholarly article
title: Linear maps preserving invertibility or related spectral properties
zbMATH Open document ID: 1045.47032
author: Peter Šemrl
author: Jinchuan Hou
publication date: 2003-11-10T00:00:00Z
review text: The authors survey some recent results about linear maps on operator algebras that preserve invertibility. They also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. Moreover, they present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, they give a negative answer to a problem posed by Gao and Hou on characterizing spectrum preserving elementary operators. Several open problems are also mentioned.
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47A10
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 2002320
zbMATH Keywords: operator algebras
zbMATH Keywords: linear preservers
zbMATH Keywords: invertibility
zbMATH Keywords: spectrum
reviewed by: Jianlian Cui
MaRDI profile type: Publication
full work available at URL: s10114-003-0269-z
OpenAlex ID: W2087203030
cites work: Propriétés spectrales des algèbres de Banach
cites work: A primer on spectral theory
cites work: Trace and spectrum preserving linear mappings in Jordan-Banach algebras
cites work: Spectrum-Preserving Linear Mappings between Banach Algebras or Jordan-Banach Algebras
cites work: Spectrum preserving linear mappings in Banach algebras
cites work: Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
cites work: On local automorphisms and mappings that preserve idempotents
cites work: Linear maps preserving the spectral radius
cites work: Invertibility preserving maps preserve idempotents
cites work: Spectral characterization of idempotents and invertibility preserving linear maps
cites work: On positive linear maps preserving invertibility
cites work: Two generalizations of the Gleason-Kahane-Żelazko theorem
cites work: On invertibility preserving linear mappings, simultaneous triangularization and property \(L\)
cites work: A characterization of homomorphisms between Banach algebras
cites work: Linear maps between Banach algebras compressing certain spectral functions
cites work: Additive maps on standard operator algebras preserving parts of the spectrum.
cites work: Sur une généralisation du groupe orthogonal à quatre variables
cites work: Q4203139
cites work: A characterization of maximal ideals
cites work: Affine mappings of invertible operators
cites work: Rank-preserving linear maps on B(X)
cites work: Spectrum-preserving elementary operators on \(B(X)\)
cites work: The spectrally bounded linear maps on operator algebras
cites work: Additive maps on standard operator algebras preserving invertibilities or zero divisors.
cites work: Jordan Homomorphisms of Rings
cites work: Spectrum-preserving linear maps
cites work: A characterization of maximal ideals in commutative Banach algebras
cites work: Q5621680
cites work: Linear Maps on Selfadjoint Operators Preserving Invertibility, Positive Definiteness, Numerical Range
cites work: Linear Transformations on Algebras of Matrices: The Invariance of the Elementary Symmetric Functions
cites work: Q4438940
cites work: Spectrum-preserving additive maps
cites work: Additive mappings preserving operators of rank one
cites work: Linear Mappings of Operator Algebras
cites work: Two characterizations of automorphisms on B(X)
cites work: Q4870717
cites work: Q4397395
cites work: Q4308112
cites work: Invertibility preserving linear maps on ℒ(𝒳)
cites work: Point-spectrum-preserving elementary operators on 𝐵(𝐻)
cites work: A characterization of multiplicative linear functionals in complex Banach algebras
cites work: Positive elementary operators compressing spectrum
DOI: 10.1007/S10114-003-0269-Z
published in: Acta Mathematica Sinica, English Series
description: scientific article; zbMATH DE number 2002320