On the reflexivity properties of Banach bundles and Banach modules

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research 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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.