On some maps into Banach algebras and Banach modules

Document Type : Research Paper


Faculty of Mathematical Sciences and Statistics, Malayer University, P.O. Box 65719-95863, Malayer, Iran



In this paper, we study some maps from a $C^*$-algebra into a Banach algebra or a Banach module. Under some conditions, by extending on unitization of Banach algebras, we prove that the maps defined into Banach algebras are homomorphisms and the others defined into Banach modules are derivations. Applications of our results in the context of $C^*$-algebras are also provided.