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<p>We show that every Banach space in which weakly compact sets are super weakly compact is automatically weakly sequentially complete answering a question from [<CitationRef CitationID="CR11">11</CitationRef>]. 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.</p>

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On Weak Sequential Completeness of Spaces Where Weakly Compact Sets are Super Weakly Compact

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月16日

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  • Zdeněk Silber

摘要

We show that every Banach space in which weakly compact sets are super weakly compact is automatically weakly sequentially complete answering a question from [11]. 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.