Preduals of JBW*-triples are 1-Plichko spaces

Abstract

We investigate the preduals of JBW*-triples from the point of view of Banach space theory. We show that the algebraic structure of a JBW*-triple M naturally yields a decomposition of its predual M*, by showing that M* is a 1-Plichko space (that is, it admits a countably 1-norming Markushevich basis). In case M is σ-finite, its predual M* is even weakly compactly generated. These results are a common roof for previous results on L1-spaces, preduals of von Neumann algebras, and preduals of JBW*-algebras.