Continuity of generalized derivations on JB*-algebras

Abstract

We prove that every generalized Jordan derivation D from a JB∗-algebra ???? into itself or into its dual space is automatically continuous. In particular, we establish that every generalized Jordan derivation from a C∗-algebra to a Jordan Banach module is continuous. As a consequence, every generalized derivation from a C∗-algebra to a Banach bimodule is continuous.