Pełczyński’s Property (V$^*$) in Lipschitz-Free Spaces

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发表日期：

2025年9月10日

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Ramón J. Aliaga,
Eva Pernecká,
Alicia Quero

摘要

We prove that Pełczyński’s property (V $^*$ $^{*}$ ) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal {F}(M)$ $F (M)$ has property (V $^*$ $^{*}$ ) when the complete metric space M is locally compact and purely 1-unrectifiable, a Hilbert space, or belongs to a class of Carnot-Carathéodory spaces satisfying a bi-Hölder condition, including Carnot groups.

Pełczyński’s Property (V\(^*\)) in Lipschitz-Free Spaces

摘要