Work

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

Year: 2026

Type: article

Abstract: 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.

Source: Results in Mathematics

DOI: 10.1007/s00025-026-02671-y

Author: Zdeněk Silber

Institutions: Czech Academy of Sciences, Czech Academy of Sciences, Institute of Mathematics

Language: English

Topic: Advanced Banach Space Theory

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: Akademie Věd České Republiky