LIE TRIPLE DERIVATIONS ON FACTOR VON NEUMANN ALGEBRAS

Liu, Lei

doi:10.4134/BKMS.2015.52.2.581

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LIE TRIPLE DERIVATIONS ON FACTOR VON NEUMANN ALGEBRAS

Journal title : Bulletin of the Korean Mathematical Society
Volume 52, Issue 2, 2015, pp.581-591
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2015.52.2.581

Title & Authors

LIE TRIPLE DERIVATIONS ON FACTOR VON NEUMANN ALGEBRAS
Liu, Lei;

Abstract

Let ${$\mathcal{A}$}$ be a factor von Neumann algebra with dimension greater than 1. We prove that if a linear map ${${\delta}:\mathcal{A}{\rightarrow}\mathcal{A}$}$ satisfies ${$${\delta}([[a,b],c])=[[{\delta}(a),b],c]+[[a,{\delta}(b),c]+[[a,b],{\delta}(c)]$$}$ for any ${$a,b,c{\in}\mathcal{A}$}$ with ab = 0 (resp. ab = P, where P is a fixed nontrivial projection of ${$\mathcal{A}$}$ ), then there exist an operator ${$T{\in}\mathcal{A}$}$ and a linear map ${$f:\mathcal{A}{\rightarrow}\mathbb{C}I$}$ vanishing at every second commutator [[a, b], c] with ab = 0 (resp. ab = P) such that ${${\delta}(a)=aT-Ta+f(a)$}$ for any ${$a{\in}\mathcal{A}$}$ .

Keywords

Lie derivations;Lie triple derivations;factor von Neumann algebras;

Language

English

Cited by

1time(s) in CrossRef

LIE -HIGHER DERIVATIONS AND LIE -HIGHER DERIVABLE MAPPINGS, Bulletin of the Australian Mathematical Society, 2017, 96, 02, 223

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