Free spaces over some proper metric spaces

Abstract

We prove that the Lipschitz-free space over a countable proper metric space is isometric to a dual space and has the metric approximation property. We also show that the Lipschitz-free space over a proper ultrametric space is isometric to the dual of a space which is isomorphic to c_0.

Cited by in corpus (6)

• On the preserved extremal structure of Lipschitz-free spaces
• Lipschitz free spaces isomorphic to their infinite sums and geometric applications
• The Metric Approximation Property and Lipschitz-Free Spaces over Subsets of ${\mathbb{R}}^N$
• Purely 1-unrectifiable metric spaces and locally flat Lipschitz functions
• Isomorphisms between spaces of Lipschitz functions
• Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete