A note on nonseparable Lipschitz-free spaces
[EN] We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson¿s property (C), Talponen¿s countable separation property, or being a G¿ateaux differentiability space. On the other hand, we single out more general pr...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/221710 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/221710 |
| Access Level: | acceso abierto |
| Palabra clave: | Lipschitz-free space Nonseparable Banach space Sequentially compact Radon Nikodym property |
| Sumario: | [EN] We prove that several classical Banach space properties are equivalent to separability for the class of Lipschitz-free spaces, including Corson¿s property (C), Talponen¿s countable separation property, or being a G¿ateaux 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¿Nikod¿ym property. |
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