Pe{\l}czy\'nski's property (V$^*$) in Lipschitz-free spaces
Functional Analysis
2026-03-17 v3
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 has property (V) when the complete metric space 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.
Cite
@article{arxiv.2411.15107,
title = {Pe{\l}czy\'nski's property (V$^*$) in Lipschitz-free spaces},
author = {Ramón J. Aliaga and Eva Pernecká and Alicia Quero},
journal= {arXiv preprint arXiv:2411.15107},
year = {2026}
}