Continuity of generalized derivations on JB*-algebras

Abstract

We prove that every generalized Jordan derivation D from a JB*-algebra A 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.

Keywords: Jordan Banach algebra, Jordan Banach module, JB*-algebra, Jordan derivation, generalized Jordan derivation, automatic continuity