On the composition of q-skew derivations in Banach algebras

Pjek Hwee Lee, Cheng Kai Liu

Research output: Contribution to journal › Article

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 languageEnglish
Pages (from-to)2413-2429
Number of pages17
JournalLinear Algebra and Its Applications
Volume434
Issue number12
DOIs
Publication statusPublished - 2011 Jun 15

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Skew Derivation
Banach algebra
Algebra
Chemical analysis
Automorphism
Generalise

All Science Journal Classification (ASJC) codes

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

Cite this

Lee, Pjek Hwee ; Liu, Cheng Kai. / On the composition of q-skew derivations in Banach algebras. In: Linear Algebra and Its Applications. 2011 ; Vol. 434, No. 12. pp. 2413-2429.
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Lee, PH & Liu, CK 2011, 'On the composition of q-skew derivations in Banach algebras', Linear Algebra and Its Applications, vol. 434, no. 12, pp. 2413-2429. https://doi.org/10.1016/j.laa.2010.12.025

On the composition of q-skew derivations in Banach algebras. / Lee, Pjek Hwee; Liu, Cheng Kai.

In: Linear Algebra and Its Applications, Vol. 434, No. 12, 15.06.2011, p. 2413-2429.

Research output: Contribution to journal › Article

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AU - Lee, Pjek Hwee

AU - Liu, Cheng Kai

PY - 2011/6/15

Y1 - 2011/6/15

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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Lee PH, Liu CK. On the composition of q-skew derivations in Banach algebras. Linear Algebra and Its Applications. 2011 Jun 15;434(12):2413-2429. https://doi.org/10.1016/j.laa.2010.12.025

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