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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.14939 |
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| _version_ | 1866916219612823552 |
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| author | Grelier, Guillaume Martín, Jaime San |
| author_facet | Grelier, Guillaume Martín, Jaime San |
| contents | For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in Böchner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With additional properties on $X$ and its norm, we show these sets are approximatively $w^*$-compact for $p\in(1,\infty)$ and even approximatively norm-compact under stronger hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximative compactness in Böchner spaces Grelier, Guillaume Martín, Jaime San Functional Analysis For any $p\in[1,\infty)$, we prove that the set of simple functions taking at most $k$ different values is proximinal in Böchner spaces $L^p(X)$ whenever $X$ is a dual Banach space with $w^*$-sequentially compact unit ball. With additional properties on $X$ and its norm, we show these sets are approximatively $w^*$-compact for $p\in(1,\infty)$ and even approximatively norm-compact under stronger hypothesis. |
| title | Approximative compactness in Böchner spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.14939 |