A study of weak^*-weak points of continuity in the unit ball of dual spaces

2025/06/10 by Soumitra Daptari, Daptari, S., Montesinos, V. +2
Mathematics · #46B10 #46B22 #46B25 #47L40 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 46A22 #Secondary 46B20

paper · pdf · doi:10.48550/arxiv.2506.08458

openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study classes of Banach spaces where the points of weak^*-weak continuity for the identity mapping on the dual unit ball form a weak^*-dense and weak^*-G_δ set. We also discuss how this property behaves in higher duals of Banach spaces. We prove in particular that if A is a von Neumann algebra and its predual has the Radon--Nikodým property, then there is no point of weak^*-weak continuity on the unit ball of A.

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