Banach spaces with weak*-sequential dual ball

2016/12/18 by Gonzalo Martínez-Cervantes, Martínez-Cervantes, Gonzalo
Mathematics · #46A50 #46B50 #54D55 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Primary 57N17 #Secondary 46B20

paper · pdf · doi:10.48550/arxiv.1612.05948

openalex publication_date 2016/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A topological space is said to be sequential if every sequentially closed subspace is closed. We consider Banach spaces with weak*-sequential dual ball. In particular, we show that if X is a Banach space with weak*-sequentially compact dual ball and Y ⊂ X is a subspace such that Y and X/Y have weak*-sequential dual ball, then X has weak*-sequential dual ball. As an application we obtain that the Johnson-Lindenstrauss space JL₂ and C(K) for K scattered compact space of countable height are examples of Banach spaces with weak*-sequential dual ball, answering in this way a question of A. Plichko.

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• On topological properties of the weak topology of a Banach space