Generalized derivations preserving quasinilpotent elements in Banach algebras

Cheng-Kai Liu, Pao Kuei Liau

Research output: Contribution to journalArticle

Abstract

Let A be a complex Banach algebra, let QA be the set of all quasinilpotent elements in A and let QA r be the set of all quasi-regular elements in A. We characterize generalized derivations g of A such that g(QA) ⊆ QA r provided that A has the property β. The class of Banach algebras with the property β is quite large: it includes C*-algebras, group algebras of locally compact groups, commutative Banach algebras, Banach algebras of all bounded linear operators on Banach spaces and so on. Our theorems are natural generalizations of the recent results for derivations obtained by Alaminos et al. [Bull. London Math. Soc. 46:379–384, 2014].

Original languageEnglish
Pages (from-to)1888-1908
Number of pages21
JournalLinear and Multilinear Algebra
Volume66
Issue number9
DOIs
Publication statusPublished - 2018 Sep 2

Fingerprint

Generalized Derivation
Banach algebra
Commutative Banach Algebra
Regular Element
Locally Compact Group
Group Algebra
Bounded Linear Operator
C*-algebra
Banach space
Theorem

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Cite this

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Generalized derivations preserving quasinilpotent elements in Banach algebras. / Liu, Cheng-Kai; Liau, Pao Kuei.

In: Linear and Multilinear Algebra, Vol. 66, No. 9, 02.09.2018, p. 1888-1908.

Research output: Contribution to journalArticle

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