On a Brešar-šemrl conjecture and derivations of banach algebras

Mikhail A. Chebotar, Wen Fong Ke, Pjek Hwee Lee

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

In this paper, we answer a question on derivations of dense algebras of linear operators posed by Brear and emrl. Our theorem implies the following result: let be a complex Banach algebra, and let d and g be continuous derivations of . If dg(x) is quasi-nilpotent for every x ∈ , then dg(x)3 lies in the radical of for every x ∈ . This result was proved by Brear and emrl with the additional assumption gd = dg.

Original languageEnglish
Pages (from-to)469-478
Number of pages10
JournalQuarterly Journal of Mathematics
Volume57
Issue number4
DOIs
Publication statusPublished - 2006 Dec

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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