Boundedness of completely additive measures with application to 2-local triple derivations

Abstract

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 derivations on associative and Jordan matrix rings over commutative rings

“…Articles [10], [22], [23] are devoted to weak-2-local derivations, and [11], [17], [18], [21] are devoted to 2-local * -Lie isomorphisms and 2-local Lie isomorphisms. A number of theorem on 2-local triple derivations were proved in [13], [15]. Other classes of 2-local maps on different types of associative and Jordan algebras were studied in [4], [7], [8], [9], [12] and [24].…”