Pełczyński's property (V$^*$) in Lipschitz-free spaces
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866908886484647936 |
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| author | Aliaga, Ramón J. Pernecká, Eva Quero, Alicia |
| author_facet | Aliaga, Ramón J. Pernecká, Eva Quero, Alicia |
| contents | We prove that Pelczyński's property (V$^*$) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal{F}(M)$ has property (V$^*$) when the complete metric space $M$ is locally compact and purely 1-unrectifiable, a Hilbert space, or belongs to a class of Carnot-Carathéodory spaces satisfying a bi-Hölder condition, including Carnot groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_15107 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pełczyński's property (V$^*$) in Lipschitz-free spaces Aliaga, Ramón J. Pernecká, Eva Quero, Alicia Functional Analysis 46B03, 46B50, 53C17 We prove that Pelczyński's property (V$^*$) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal{F}(M)$ has property (V$^*$) when the complete metric space $M$ is locally compact and purely 1-unrectifiable, a Hilbert space, or belongs to a class of Carnot-Carathéodory spaces satisfying a bi-Hölder condition, including Carnot groups. |
| title | Pełczyński's property (V$^*$) in Lipschitz-free spaces |
| topic | Functional Analysis 46B03, 46B50, 53C17 |
| url | https://arxiv.org/abs/2411.15107 |