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arXiv · 1612.05948

Banach spaces with weak*-sequential dual ball

Gonzalo Martínez-Cervantes
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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 $Y \subset X$ 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 $JL_2$ 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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Gonzalo Martínez-Cervantes. 2016-12-18. Banach spaces with weak*-sequential dual ball. https://arxiv.org/abs/1612.05948

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