Lipschitz Free Spaces over Locally Compact Metric Spaces

Abstract

We prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikodým property. We also show that the Lipschitz free space over a complete, locally compact metric space has the Schur or approximation property whenever the Lipschitz free space over each compact subset also has this property.

27 pages. Changes to names of some objects and addition of informal discussion of semi-embedding theorem. Implemented referee's corrections