Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.14939 |
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Inhaltsangabe:
- 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.