Maps preserving the truncation of triple products on Cartan factors

Abstract: We generalize the concept of truncation of operators to JB*-triples and study some general properties of bijections preserving the truncation of triple products in both directions between general JB*-triples. In our main result we show that a (non-necessarily linear nor continuous) bijection between atomic JBW*-triples preserving the truncation of triple products in both directions (and such that the restriction to each rank-one Cartan factor is a continuous mapping) is an isometric real linear triple isomorphism.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar