Pełczyński's property (V^*) in Lipschitz-free spaces

2024/11/22 by Ramón J. Aliaga, Eva Pernecká, Aliaga, Ramón J. +3 · 1 citation
Mathematics · #46B03 #46B50 #53C17 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2411.15107

openalex publication_date 2024/11/22 · openalex created_date 2024/12/04 · openalex updated_date 2026/07/30

Abstract

We prove that Pelczyński's property (V^*) is locally determined for Lipschitz-free spaces, and obtain several sufficient conditions for it to hold. We deduce that 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.

Cited by

• Lipschitz spaces over non-porous sets

Related

• Pełczyński space is isomorphic to the Lipschitz free space over a compact set
• Lipschitz Free Spaces over Locally Compact Metric Spaces
• Products of Lipschitz-free spaces and applications
• Pełczyński's type sets and Pełczyński's geometrical properties of locally convex spaces
• Quantification of Pełczyński's property (V)