On the weak∗ separability of the space of Lipschitz functions

被引：0

作者：

Candido, Leandro ^{[1
]}

Cuth, Marek ^{[2
]}

Vejnar, Benjamin ^{[2
]}

机构：

[1] Univ Fed Sao Paulo UNIFESP, Dept Matemat, Inst Ciencia & Tecnol, Sao Jose Dos Campos, SP, Brazil

[2] Charles Univ Prague, Fac Math & Phys, Dept Math Anal, Sokolovska 83, Prague 8, Czech Republic

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2025年 / 289卷 / 01期

基金：

巴西圣保罗研究基金会;

关键词：

Lipschitz function; Lipschitz-free space; Nonseparable Banach spaces; Weak* topology; BANACH-SPACES; EMBEDDINGS;

D O I：

10.1016/j.jfa.2025.110925

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We conjecture that whenever M is a metric space of density at most continuum, then the space of Lipschitz functions is w & lowast;- separable. We prove the conjecture for several classes of metric spaces including all the Banach spaces with a projectional skeleton, Banach spaces with a w & lowast;-separable dual unit ball and locally separable complete metric spaces. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

引用

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