Pełczyński's property (V${}^{\ast }$) in Lipschitz-free spaces

Abstract

We prove that Pelczyński's property (V${}^{\ast }$) 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${}^{\ast }$) 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.

References in corpus (2)

• Delta-points and their implications for the geometry of Banach spaces
• De Leeuw representations of functionals on Lipschitz spaces

Cited by in corpus (1)

• Lipschitz spaces over non-porous sets