An Asplund space with norming Markuševič basis that is not weakly compactly generated

Abstract

We construct an Asplund Banach space $\mathcal{X}$ with a norming Markuševič basis such that $\mathcal{X}$ is not weakly compactly generated. This solves a long-standing open problem from the early nineties, originally due to Gilles Godefroy. En route to the proof, we construct a peculiar example of scattered compact space, that also solves a question due to Wiesław Kubiś and Arkady Leiderman.

References in corpus (1)

• Small semi-Eberlein compacta and inverse limits

Cited by in corpus (3)

• Rotund Gateaux smooth norms which are not locally uniformly rotund
• Banach spaces of continuous functions without norming Markushevich bases
• Small semi-Eberlein compacta and inverse limits