Infinite dimensional spaces in the set of strongly norm-attaining Lipschitz maps

IF 1.3 2区数学 Q1 MATHEMATICS

Revista Matematica Iberoamericana Pub Date : 2022-04-26 DOI:10.4171/rmi/1425

Antonio Avil'es, Gonzalo Mart'inez-Cervantes, A. R. Zoca, P. Tradacete

引用次数: 1

Abstract

We prove that if $M$ is an infinite complete metric space then the set of strongly norm-attaining Lipschitz functions $\SA(M)$ contains a linear subspace isomorphic to $c_0$. This solves an open question posed by V. Kadets and O. Rold\'an.

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强范数达到的Lipschitz映射集合中的无限维空间

证明了如果$M$是一个无限完备度量空间，则强范数达到的Lipschitz函数集$\SA(M)$包含一个同构于$c_0$的线性子空间。这就解决了立宪民主党人和罗尔德安提出的一个悬而未决的问题。

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

Revista Matematica Iberoamericana 数学-数学

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.