Spectrally bounded φ-derivations on Banach algebras
Journal
Proceedings of the American Mathematical Society
Journal Volume
133
Journal Issue
5
Pages
1427-1435
Date Issued
2005
Author(s)
Liu, C.-K.
Abstract
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. © 2004 American Mathematical Society.
Type
journal article