Abstract
We prove a Jordan version of Dorofeev’s boundedness theorem for completely additive measures and use it to show that every (not necessarily linear nor continuous) 2-local triple derivation on a continuous JBW∗-triple is a triple derivation. 2-local triple derivations are well understood on von Neumann algebras. JBW*-triples, which are properly defined in Section I, are intimately related to infinite dimensional holomorphy and include von Neumann algebras as special cases. In particular, continuous JBW∗-triples can be realized as subspaces of continuous von Neumann algebras which are stable for the triple product xy∗z + zy∗x and closed in the weak operator topology.
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