Compactness in Banach space theory - selected problems

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-Nikodým compacta.

Keywords

• Hilbertian ball
• euclidean ball
• Eberlein compact
• uniform Eberlein compact
• discontinuous norms
• weakly compactly generated space
• Valdivia compact
• Radon-Nikodym compact