On the reflexivity properties of Banach bundles and Banach modules
| Autor: | Lučić, Milica, Pasqualetto, Enrico, Vojnović, Ivana |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper we investigate some reflexivity-type properties of separable measurable Banach bundles over a $\sigma$-finite measure space. Our two main results are the following: - The fibers of a bundle are uniformly convex (with a common modulus of convexity) if and only if the space of its $L^p$-sections is uniformly convex for every $p\in(1,\infty)$. - The fibers of a bundle are reflexive if and only if the space of its $L^p$-sections is reflexive. These results generalise the well-known corresponding ones for Lebesgue-Bochner spaces. Comment: 25 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|