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arXiv · 2501.16855

On weak sequential completeness of spaces where weakly compact sets are super weakly compact

Zdeněk Silber
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Abstract

We show that every Banach space in which weakly compact sets are super weakly compact in automatically weakly sequentially complete answering a question by Silber (2024). In the proof we show how to build a weakly compact set which is not super weakly compact from an arbitrary nontrivial weakly Cauchy sequence using the notion of a summing subsequence of Rosenthal or Singer.

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Zdeněk Silber. 2025-01-28. On weak sequential completeness of spaces where weakly compact sets are super weakly compact. https://arxiv.org/abs/2501.16855

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