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

@article{Peralta2012AutomaticCO,
  title={Automatic continuity of derivations on C*-algebras and JB*-triples},
  author={Antonio M. Peralta and Bernard Russo},
  journal={arXiv: Operator Algebras},
  year={2012}
}
We introduce the notion of a 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… 
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