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arXiv · 2007.14201

An Asplund space with norming Marku\v{s}evi\v{c} basis that is not weakly compactly generated

Petr Hájek·Tommaso Russo·Jacopo Somaglia·Stevo Todorčević
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Abstract

We construct an Asplund Banach space $\mathcal{X}$ with a norming Marku\v{s}evi\v{c} 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 Wies{\l}aw Kubi\'s and Arkady Leiderman.

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Petr Hájek, Tommaso Russo, Jacopo Somaglia, Stevo Todorčević. 2020-07-28. An Asplund space with norming Marku\v{s}evi\v{c} basis that is not weakly compactly generated. https://doi.org/10.1016/j.aim.2021.108041

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