On generalized derivations in Banach algebras
Volume 194 / 2009
Studia Mathematica 194 (2009), 81-89
MSC: 47B47, 47B48.
DOI: 10.4064/sm194-1-5
Abstract
We study generalized derivations $G$ defined on a complex Banach algebra $A$ such that the spectrum $\sigma (Gx)$ is finite for all $x \in A$. In particular, we show that if $A$ is unital and semisimple, then $G$ is inner and implemented by elements of the socle of $A$.
