Abstract

Let A be a Banach algebra and M be a Banach right A-module. A linear map δ:M→M is called a generalized derivation if there exists a derivation d:A→A such that

In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on Mand derivations on T. In particular, we prove that the so-called generalized first cohomology group of M is isomorphic to the first cohomology group of T.