Characterizations of Lie derivations of \(B(X)\)
type: Item
instance of: scholarly article
title: Characterizations of Lie derivations of \(B(X)\)
zbMATH Open document ID: 1188.47029
author: Fangyan Lu
author: Wu Jing
published in: Linear Algebra and its Applications
publication date: 2009-12-18T00:00:00Z
review text: The authors study a variant of the concept of a Lie derivation in the setting of bounded linear operators on a Banach space \(X\) of dimension at least~\(3\). The two results proven in this paper state that, if \(\delta: B(X)\to B(X)\) is a linear mapping satisfying the Lie derivation property on commutators \([a,b]\) with (i) \(ab=0\) or (ii) \(ab\) is a fixed non-trivial idempotent~\(p\), then \(\delta\) is the sum of a derivation \(d\) on \(B(X)\) and a linear centre-valued mapping \(\tau\) vanishing on commutators \([a,b]\) satisfying (i) or (ii), respectively.
reviewed by: Martin Mathieu
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47L10
zbMATH DE Number: 5650021
zbMATH Keywords: Lie derivation
zbMATH Keywords: derivation
zbMATH Keywords: centre-valued trace
MaRDI profile type: Publication
full work available at URL: j.laa.2009.07.026
OpenAlex ID: W2086729240
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Wikidata QID: Q115344858
DOI: 10.1016/J.LAA.2009.07.026
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description: scientific article; zbMATH DE number 5650021