On the composition of q-skew derivations in Banach algebras

Pjek Hwee Lee; Cheng Kai Liu

doi:10.1016/j.laa.2010.12.025

On the composition of q-skew derivations in Banach algebras

Pjek Hwee Lee, Cheng Kai Liu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let A be a Banach algebra, let σ be an automorphism of A, and let d, δ be q-skew σ-derivations of A. We show that if dδ(a) is quasi-nilpotent for any a∈A, then dδ(a)3 lies in the radical of A for all a∈A. This result simultaneously generalizes the previous results obtained by Brešar and Šemrl [5], Chebotar et al. [7] and Abdelali [1].

Original language	English
Pages (from-to)	2413-2429
Number of pages	17
Journal	Linear Algebra and Its Applications
Volume	434
Issue number	12
DOIs	https://doi.org/10.1016/j.laa.2010.12.025
Publication status	Published - 2011 Jun 15

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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abstract = "Let A be a Banach algebra, let σ be an automorphism of A, and let d, δ be q-skew σ-derivations of A. We show that if dδ(a) is quasi-nilpotent for any a∈A, then dδ(a)3 lies in the radical of A for all a∈A. This result simultaneously generalizes the previous results obtained by Bre{\v s}ar and {\v S}emrl [5], Chebotar et al. [7] and Abdelali [1].",

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AU - Liu, Cheng Kai

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N2 - Let A be a Banach algebra, let σ be an automorphism of A, and let d, δ be q-skew σ-derivations of A. We show that if dδ(a) is quasi-nilpotent for any a∈A, then dδ(a)3 lies in the radical of A for all a∈A. This result simultaneously generalizes the previous results obtained by Brešar and Šemrl [5], Chebotar et al. [7] and Abdelali [1].

AB - Let A be a Banach algebra, let σ be an automorphism of A, and let d, δ be q-skew σ-derivations of A. We show that if dδ(a) is quasi-nilpotent for any a∈A, then dδ(a)3 lies in the radical of A for all a∈A. This result simultaneously generalizes the previous results obtained by Brešar and Šemrl [5], Chebotar et al. [7] and Abdelali [1].

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