On the composition of q-skew derivations in Banach algebras
Resource
Linear Algebra and its Applications, 434(12), 2413-2429
Journal
Linear Algebra and its Applications
Journal Volume
434
Journal Issue
12
Pages
2413-2429
Date Issued
2011
Date
2011
Author(s)
Lee, Pjek-Hwee
Liu, Cheng-Kai
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]. © 2011 Published by Elsevier Inc.
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]. © 2011 Published by Elsevier Inc.
Type
journal article
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