Automatic continuity of derivations on C*-algebras and JB*-triples

We introduce the notion of a Banach Jordan triple module and determine the precise conditions under which every derivation from a JB*-triple E into a Banach Jordan triple E-module is continuous. In particular, every derivation from a real or complex JB*-triple into its dual space is automatically continuous. Among the consequences, we prove that every triple derivation from a C*-algebra A to a Banach triple A-module is continuous. In particular, every Jordan derivation from A to a Banach A-bimodule is a derivation, a result which complements a classical theorem due to B.E. Johnson.

(This paper has appeared in J. Algebra 399 (2014), 960-977)


Antonio M. Peralta < aperalta@ugr.es >

Bernard Russo < brusso@math.uci.edu >