Lie derivations on Banach algebras
type: Item
instance of: scholarly article
title: Lie derivations on Banach algebras
zbMATH Open document ID: 0957.46032
author: Armando R. Villena
published in: Journal of Algebra
publication date: 2000-05-08T00:00:00Z
review text: A Lie derivation \(\Delta\) on a unital complex Banach algebra \(A\) is considered. The main result of the article is the following Theorem. Let \(D\) be a Lie derivation on a unital complex Banach algebra \(A\). Then for every primitive ideal \(P\) of \(A\), except for a finite set of them which have finite codimension greater than one, there exist a derivation \(d\) from \(A/P\) to itself and a linear functional \(\tau\) on \(A\) such that \[ Q_p\Delta(a)= d(a+ P)+ \tau(a) \] for all \(a\in A\) (where \(Q_p\) denotes the quotient map from \(A\) onto \(A(p)\). Moreover, the preceding decomposition holds for all primitive ideals in the case where \(\Delta\) is continuous.
Mathematics Subject Classification ID: 46H05
zbMATH DE Number: 1441815
zbMATH Keywords: Lie derivation
zbMATH Keywords: unital complex Banach algebra
zbMATH Keywords: primitive ideal
Wikidata QID: Q115395779
reviewed by: Andreiy Kondrat'yev
MaRDI profile type: Publication
OpenAlex ID: W2139500330
cites work: Prime ideals and automatic continuity problems for Banach algebras
cites work: Commutativity preserving mappings on semiprime rings
cites work: Continuity of Lie derivations on Banach algebras
cites work: Commuting Traces of Biadditive Mappings, Commutativity-Preserving Mappings and Lie Mappings
cites work: Continuity of Systems of Derivations on F-Algebras
cites work: Lie and Jordan structures in simple associative rings
cites work: Continuity of Derivations and a Problem of Kaplansky
cites work: Continuity of Higher Derivations
cites work: Q4308104
cites work: Lie derivations of primitive rings
cites work: Higher Derivations on Banach Algebras
cites work: Q4293544
cites work: Derivations on commutative normed algebras
cites work: The image of a derivation is contained in the radical
cites work: Primitive ideals and derivations on non-commutative Banach algebras
DOI: 10.1006/JABR.1999.8193
Recommended article: Continuity of Lie derivations on Banach algebras
Recommended article: On the range of a lie derivation on a banach algebra
Recommended article: Derivations on Banach algebras
Recommended article: Q4720217
Recommended article: ON DERIVATIONS IN BANACH ALGEBRAS
Recommended article: Banach Lie algebroids
Recommended article: LIE-TYPE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES AND RELATED TOPICS
Recommended article: Derivations in Banach algebras
Recommended article: Q4658644
Recommended article: Derivations from Banach algebras
description: scientific article; zbMATH DE number 1441815