An Asplund space with norming Markuševič basis that is not weakly compactly generated
| Autor: | Tommaso Russo, Stevo Todorcevic, Petr Hájek, Jacopo Somaglia |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Mathematics::Functional Analysis
0209 industrial biotechnology Pure mathematics Basis (linear algebra) General Mathematics Open problem 010102 general mathematics Banach space 02 engineering and technology Construct (python library) 01 natural sciences Mathematics - Functional Analysis 020901 industrial engineering & automation Compact space 0101 mathematics Mathematics Asplund space |
| Zdroj: | Advances in Mathematics. 392:108041 |
| ISSN: | 0001-8708 |
| DOI: | 10.1016/j.aim.2021.108041 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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