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 language | English |
|---|---|
| Pages (from-to) | 1888-1908 |
| Number of pages | 21 |
| Journal | Linear and Multilinear Algebra |
| Volume | 66 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2018 Sep 2 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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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 journal › Article
TY - JOUR
T1 - Generalized derivations preserving quasinilpotent elements in Banach algebras
AU - Liu, Cheng-Kai
AU - Liau, Pao Kuei
PY - 2018/9/2
Y1 - 2018/9/2
N2 - 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].
AB - 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].
UR - http://www.scopus.com/inward/record.url?scp=85029719617&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85029719617&partnerID=8YFLogxK
U2 - 10.1080/03081087.2017.1376613
DO - 10.1080/03081087.2017.1376613
M3 - Article
VL - 66
SP - 1888
EP - 1908
JO - Linear and Multilinear Algebra
JF - Linear and Multilinear Algebra
SN - 0308-1087
IS - 9
ER -