Lipschitz Free Spaces over Locally Compact Metric Spaces
Functional Analysis
2021-02-12 v3 Metric Geometry
Abstract
We prove that the Lipschitz free space over a certain type of discrete metric space has the Radon-Nikod\'ym 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.
Cite
@article{arxiv.2004.11951,
title = {Lipschitz Free Spaces over Locally Compact Metric Spaces},
author = {Chris Gartland},
journal= {arXiv preprint arXiv:2004.11951},
year = {2021}
}
Comments
27 pages. Changes to names of some objects and addition of informal discussion of semi-embedding theorem. Implemented referee's corrections