Banach空间的渐近平滑性、集中性质及其应用

IF 1.7 2区数学 Q1 MATHEMATICS Journal of Functional Analysis Pub Date : 2024-11-20 DOI:10.1016/j.jfa.2024.110763

A. Fovelle

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引用次数: 0

摘要

我们证明了在Hamming图上定义的Lipschitz映射在Banach空间中某些浓度性质在p和下稳定性的最优结果。作为应用，我们给出了Szlenk指数任意高的空间的例子，这些空间仍然具有集中性质。特别地，我们得到了第一个具有集中但不具有渐近光滑性的Banach空间的例子。

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Asymptotic smoothness, concentration properties in Banach spaces and applications

We prove an optimal result of stability under

ℓ_{p}

-sums of some concentration properties for Lipschitz maps defined on Hamming graphs into Banach spaces. As an application, we give examples of spaces with Szlenk index arbitrarily high that admit nevertheless a concentration property. In particular, we get the very first examples of Banach spaces with concentration but without asymptotic smoothness property.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis

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