Extreme points in Lipschitz-free spaces over compact metric spaces
Functional Analysis
2022-03-16 v2
Abstract
We prove that all extreme points of the unit ball of a Lipschitz-free space over a compact metric space have finite support. Combined with previous results, this completely characterizes extreme points and implies that all of them are also extreme points in the bidual ball. For the proof, we develop some properties of an integral representation of functionals on Lipschitz spaces originally due to K. de Leeuw.
Keywords
Cite
@article{arxiv.2102.01219,
title = {Extreme points in Lipschitz-free spaces over compact metric spaces},
author = {Ramón J. Aliaga},
journal= {arXiv preprint arXiv:2102.01219},
year = {2022}
}
Comments
v2: Corrected an embarrassing amount of small errors in the first draft