Measures of weak non-compactness in preduals of von Neumann algebras and JBW*-triples

Abstract

We prove, among other results, that three standard measures of weak non-compactness coincide in preduals of JBW*-triples. This result is new even for preduals of von Neumann algebras.

We further provide a characterization of JBW*-triples with strongly WCG predual and describe the order of seminorms defining the strong* topology. As a byproduct we improve a characterization of weakly compact subsets of a JBW*-triple predual, providing so a proof for a conjecture, open for almost eighteen years, on weakly compact operators from a JB*-triple into a complex Banach space.

Keywords

• Measure of weak non-compactness
• Von Neumann algebra
• JBW*-triple
• Strong* topology