Ring isomorphisms and linear or additive maps preserving zero products on nest algebras
type: Item
instance of: scholarly article
title: Ring isomorphisms and linear or additive maps preserving zero products on nest algebras
zbMATH Open document ID: 1061.47035
published in: Linear Algebra and its Applications
publication date: 2004-08-04T00:00:00Z
review text: In this paper, the autors show that every ring isomorphism between norm closed standard subalgebras of nest algebras acting on infinite-dimensional Banach spaces is either a spatial isomorphism or a spatial conjugate isomorphism. This is then used to characterize the linear or additive maps between nest algebras which preserve zero products.
Mathematics Subject Classification ID: 47B49
Mathematics Subject Classification ID: 47L35
zbMATH DE Number: 2081252
zbMATH Keywords: additive preservers
zbMATH Keywords: zero products
zbMATH Keywords: standard operator algebras
author: Jinchuan Hou
author: Xiu-Ling Zhang
reviewed by: Jianlian Cui
MaRDI profile type: Publication
full work available at URL: j.laa.2004.02.032
OpenAlex ID: W2017497858
cites work: Maps preserving numerical radius distance on C*-algebras
cites work: Numerical radius distance-preserving maps on $\mathcal {B}(H)$
cites work: Additive rank-one preserving mappings on triangular matrix algebras
cites work: Mappings preserving zero products
cites work: Q4780583
cites work: Linear maps on von Neumann algebras preserving zero products on tr-rank
cites work: Non-linear numerical radius isometries on atomic nest algebras and diagonal algebras.
cites work: Q3610806
cites work: Local multiplications on algebras spanned by idempotents
cites work: Q3154055
cites work: Rank-preserving linear maps on B(X)
cites work: Rank-1 preserving linear maps on nest algebras.
cites work: Additive mappings decreasing rank one
cites work: Multiplicative mappings of operator algebras
cites work: Orthogonality preserving transformations on indefinite inner product spaces: Generalization of Uhlhorn's version of Wigner's theorem
cites work: On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in L²
cites work: On Some Algebras of Operators. II
cites work: Maps on simple algebras preserving zero products. I: The associative case
cites work: Linear mappings preserving square-zero matrices
cites work: Generalizations of Certain Nest Algebra Results
DOI: 10.1016/J.LAA.2004.02.032
description: scientific article; zbMATH DE number 2081252