We construct an Asplund Banach space X with a norming Markusevic basis such that 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 Wieslaw Kubis and Arkady Leiderman. (c) 2021 Elsevier Inc. All rights reserved.
An Asplund space with norming Markusevic basis that is not weakly compactly generated
Somaglia, J;
2021-01-01
Abstract
We construct an Asplund Banach space X with a norming Markusevic basis such that 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 Wieslaw Kubis and Arkady Leiderman. (c) 2021 Elsevier Inc. All rights reserved.File in questo prodotto:
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Hajek, Russo, Somaglia, Todorcevic - An Asplund space with norming Markushevich basis that is not weakly compactly generated.pdf
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