Local triple derivations on C∗-algebras and JB∗-triples

Abstract

In a first result we prove that every continuous local triple derivation on a\nJB$^*$-triple is a triple derivation. We also give an automatic continuity\nresult, that is, we show that local triple derivations on a JB$^*$-triple are\ncontinuous even if not assumed a priori to be so. In particular every local\ntriple derivation on a C$^*$-algebra is a triple derivation. We also explore\nthe connections between (bounded local) triple derivations and generalised\n(Jordan) derivations on a C$^*$-algebra.\n