On the weak$^*$ separability of the space of Lipschitz functions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910873290801152 |
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| author | Candido, Leandro Cuth, Marek Vejnar, Benjamin |
| author_facet | Candido, Leandro Cuth, Marek Vejnar, Benjamin |
| contents | We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a $w^*$-separable dual unit ball and locally separable complete metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03982 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the weak$^*$ separability of the space of Lipschitz functions Candido, Leandro Cuth, Marek Vejnar, Benjamin Functional Analysis 46B26, 51F30, 54E50 (primary), and 46B80, 46B20 (secondary) We conjecture that whenever $M$ is a metric space of density at most continuum, then the space of Lipschitz functions is $w^*$-separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a $w^*$-separable dual unit ball and locally separable complete metric spaces. |
| title | On the weak$^*$ separability of the space of Lipschitz functions |
| topic | Functional Analysis 46B26, 51F30, 54E50 (primary), and 46B80, 46B20 (secondary) |
| url | https://arxiv.org/abs/2406.03982 |