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arXiv · 2411.15107

Pe{\l}czy\'nski's property (V$^*$) in Lipschitz-free spaces

Ramón J. Aliaga·Eva Pernecká·Alicia Quero
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Abstract

We prove that Pelczy\'nski's property (V$^*$) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that $\mathcal{F}(M)$ 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-Carath\'eodory spaces satisfying a bi-H\"older condition, including Carnot groups.

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Ramón J. Aliaga, Eva Pernecká, Alicia Quero. 2024-11-22. Pe{\l}czy\'nski's property (V$^*$) in Lipschitz-free spaces. https://doi.org/10.1007/s00025-025-02510-6

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