Article
| Title: | A note on nonseparable Lipschitz-free spaces (English) |
| Author: | Aliaga, Ramón J. |
| Author: | Grelier, Guillaume |
| Author: | Procházka, Antonín |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 65 |
| Issue: | 1 |
| Year: | 2024 |
| Pages: | 31-44 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson's property ($\mathcal{C}$), Talponen's countable separation property, or being a Gâteaux differentiability space. On the other hand, we single out more general properties where this equivalence fails. In particular, the question whether the duals of nonseparable Lipschitz-free spaces have a weak$^*$ sequentially compact ball is undecidable in ZFC. Finally, we provide an example of a nonseparable dual Lipschitz-free space that fails the Radon--Nikodým property. (English) |
| Keyword: | Lipschitz-free space |
| Keyword: | nonseparable Banach space |
| Keyword: | sequentially compact |
| Keyword: | Radon--Nikodým property |
| MSC: | 46B20 |
| MSC: | 46B26 |
| MSC: | 46E15 |
| DOI: | 10.14712/1213-7243.2025.003 |
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| Date available: | 2025-04-24T07:46:11Z |
| Last updated: | 2025-04-25 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152942 |
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