We construct an Asplund Banach space with a norming Markuševič basis such that 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.

An Asplund space with norming Markuševič basis that is not weakly compactly generated / P. Hájek, T. Russo, J. Somaglia, S. Todorčević. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 392(2021 Dec 03), pp. 108041.1-108041.22. [10.1016/j.aim.2021.108041]

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

T. Russo
Secondo
;
J. Somaglia
Penultimo
;
2021

Abstract

We construct an Asplund Banach space with a norming Markuševič basis such that 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.
Norming Markuševič basis; Asplund Banach space; Weakly compactly generated Banach space; ϱ-function; Semi-Eberlein compact space;
Settore MAT/05 - Analisi Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/871230
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