On weak sequential completeness of spaces where weakly compact sets are super weakly compact
Functional Analysis
2025-01-29 v1
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.
Keywords
Cite
@article{arxiv.2501.16855,
title = {On weak sequential completeness of spaces where weakly compact sets are super weakly compact},
author = {Zdeněk Silber},
journal= {arXiv preprint arXiv:2501.16855},
year = {2025}
}