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arXiv · 1901.08056

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

Jan Hamhalter·Ondřej F. K. Kalenda·Antonio M. Peralta·Hermann Pfitzner
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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.

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Jan Hamhalter, Ondřej F. K. Kalenda, Antonio M. Peralta, Hermann Pfitzner. 2019-01-23. Measures of weak non-compactness in preduals of von Neumann algebras and JBW$^*$-triples. https://doi.org/10.1016/j.jfa.2019.108300

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