Extreme points in Lipschitz-free spaces over compact metric spaces

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.

arXiv commentv2: Corrected an embarrassing amount of small errors in the first draft

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Cited by in corpus (3)

• Residuality in the set of norm attaining operators between Banach spaces
• Convex integrals of molecules in Lipschitz-free spaces
• De Leeuw representations of functionals on Lipschitz spaces