Compactness in Banach space theory - selected problems
Antonio Avil\'es, Ond\v{r}ej F.K. Kalenda
TL;DR
This paper reviews key open problems related to various forms of compactness in nonseparable Banach spaces, including topics like weak topology, function spaces, and special classes of compacta.
Contribution
It compiles and discusses several important unresolved problems in the theory of compactness within nonseparable Banach spaces.
Findings
Identifies open problems in weak topology of Hilbertian balls
Highlights issues in spaces of continuous functions on Eberlein compacta
Discusses challenges in Radon-Nikodým and Valdivia compacta
Abstract
We list a number of problems in several topics related to compactness in nonseparable Banach spaces. Namely, about the Hilbertian ball in its weak topology, spaces of continuous functions on Eberlein compacta, WCG Banach spaces, Valdivia compacta and Radon-Nikod\'{y}m compacta.
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