On weak sequential completeness of spaces where weakly compact sets are super weakly compact
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915126351757312 |
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| author | Silber, Zdeněk |
| author_facet | Silber, Zdeněk |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_16855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On weak sequential completeness of spaces where weakly compact sets are super weakly compact Silber, Zdeněk Functional Analysis 46B03, 46B20, 46B50 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. |
| title | On weak sequential completeness of spaces where weakly compact sets are super weakly compact |
| topic | Functional Analysis 46B03, 46B20, 46B50 |
| url | https://arxiv.org/abs/2501.16855 |