TY - JOUR
T1 - Spectrally bounded φ-derivations on Banach algebras
AU - Lee, Tsiu Kwen
AU - Liu, Cheng Kai
N1 - Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005/5
Y1 - 2005/5
N2 - Applying the density theorem on algebras with φ-derivations, we show that if a φ-derivation δ of a unital Banach algebra A is spectrally bounded, then [δ(A), A] ⊆ rad(A). Also, δ(A) ⊆ rad(A) if and only if sup{r(z-1δ(z)) | z ε A is invertible} < ∞, where r(a) denotes the spectral radius of a ε A.
AB - Applying the density theorem on algebras with φ-derivations, we show that if a φ-derivation δ of a unital Banach algebra A is spectrally bounded, then [δ(A), A] ⊆ rad(A). Also, δ(A) ⊆ rad(A) if and only if sup{r(z-1δ(z)) | z ε A is invertible} < ∞, where r(a) denotes the spectral radius of a ε A.
UR - http://www.scopus.com/inward/record.url?scp=18144404308&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18144404308&partnerID=8YFLogxK
U2 - 10.1090/S0002-9939-04-07655-5
DO - 10.1090/S0002-9939-04-07655-5
M3 - Article
AN - SCOPUS:18144404308
VL - 133
SP - 1427
EP - 1435
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
SN - 0002-9939
IS - 5
ER -