Boundedness of completely additive measures with application to 2-local triple derivations
Jan HamhalterCzech Technical University in Prague 1 , Faculty of Electrical Engineering, Technicka 2, 166 27, Prague 6, Czech RepublicKarimbergen KudaybergenovKarakalpak State University 2 Ch. Abdirov 1, Department of Mathematics, , Nukus 230113, UzbekistanAntonio M. PeraltaUniversidad de Granada 3 Departamento de Análisis Matemático, Facultad de Ciencias, , 18071 Granada, SpainBernard RussoUniversity of California 4 Department of Mathematics, , Irvine, California 92697-3875, USA
ABI
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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