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 >