Local derivations of nest subalgebras of von Neumann algebras
type: Item
instance of: scholarly article
title: Local derivations of nest subalgebras of von Neumann algebras
zbMATH Open document ID: 1067.46063
published in: Linear Algebra and its Applications
publication date: 2004-11-26T00:00:00Z
review text: Let \(\delta\colon A\rightarrow M\) be a linear map from an algebra \(A\) into an \(A\)-bimodule \(M\). The map \(\delta\) is said to be a local derivation if for each \(a\in A\) there exists a derivation \(\delta_a: A\rightarrow M\) such that \(\delta(a)=\delta_a(a)\). It is said to be a 2-local derivation if for all \(a,b\in A\) there exists a derivation \(\delta_{a,b}\colon A\rightarrow M\) such that \(\delta(a)=\delta_{a,b}(a)\) and \(\delta(b)=\delta_{a,b}(b)\). In the paper under review, it is shown that if \(M\) is a factor von Neumann algebra and \(A\) is a nest subalgebra of \(M\), then any continuous local derivation and any 2-local derivation from \(A\) into \(M\) are necessarily derivations.
reviewed by: Armando R. Villena
Mathematics Subject Classification ID: 46L57
Mathematics Subject Classification ID: 47B47
zbMATH DE Number: 2119128
zbMATH Keywords: derivation
zbMATH Keywords: local derivation
zbMATH Keywords: 2-local derivation
zbMATH Keywords: von Neumann algebra
zbMATH Keywords: nest subalgebra
author: Jianhua Zhang
author: Guoxing Ji
author: Huai-Xin Cao
MaRDI profile type: Publication
full work available at URL: j.laa.2004.05.015
OpenAlex ID: W2043509255
cites work: Reflexivity, Algebraic Reflexivity and Linear Interpolation
cites work: Local derivations
cites work: Local derivations on operator algebras
cites work: The set of automorphisms of B(H) is topologically reflexive in B(B(H))
cites work: Mappings which Preserve Idempotents, Local Automorphisms, and Local Derivations
cites work: Q3198400
cites work: Local automorphisms and derivations on $\mathcal {B}(H)$
cites work: Nest-subalgebras of von Neumann algebras
cites work: Derivations of nest algebras
cites work: Jordan Derivations of Prime Rings
cites work: Jordan Derivations on Semiprime Rings
cites work: Derivations of \(W^ *\)-algebras
cites work: Q3667432
cites work: Q3927697
cites work: Q3994569
DOI: 10.1016/J.LAA.2004.05.015
description: scientific article; zbMATH DE number 2119128