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arXiv · 2205.11608

On the reflexivity properties of Banach bundles and Banach modules

Milica Lučić·Enrico Pasqualetto·Ivana Vojnović
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Abstract

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.

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Milica Lučić, Enrico Pasqualetto, Ivana Vojnović. 2022-05-23. On the reflexivity properties of Banach bundles and Banach modules. https://arxiv.org/abs/2205.11608

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