On the reflexivity properties of Banach bundles and Banach modules

IF 1.1 2区数学 Q1 MATHEMATICS Banach Journal of Mathematical Analysis Pub Date : 2023-12-15 DOI:10.1007/s43037-023-00315-9

Milica Lučić, Enrico Pasqualetto, Ivana Vojnović

引用次数: 0

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 for every $p\in (1,\infty )$.

They generalise well-known results for Lebesgue–Bochner spaces.

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论巴拿赫束和巴拿赫模块的反射特性

在本文中，我们研究了在（\sigma \）无限度量空间上的可分离可度量巴拿赫束的一些反射型性质。我们的两个主要结果如下：当且仅当它的 $L^p$-section 空间对于每一个 $p\in (1,\infty )$ 都是均匀凸的时候，束的纤维才是均匀凸的（具有共同的凸模）。当且仅当对于每一个（p\in (1,\infty)）来说，它的$L^p$-截面的空间是反折的时候，束的纤维才是反折的。它们概括了 Lebesgue-Bochner 空间的著名结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Banach Journal of Mathematical Analysis 数学-数学

CiteScore

2.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group. Banach J. Math. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.

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