On exposed points of Lipschitz free spaces

2018/10/29 by Colin Petitjean, Petitjean, Colin, A. Procházka +1
Mathematics · #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1810.12031

openalex publication_date 2018/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that a molecule d(x,y)^-1(δ(x)-δ(y)) is an exposed point of the unit ball of a Lispchitz free space \mathcal F(M) if and only if the metric segment [x,y]=\z ∈ M : d(x,y)=d(z,x)+d(z,y) \ is reduced to \x,y\. This is based on a recent result due to Aliaga and Pernecká which states that the class of Lipschitz free spaces over closed subsets of M is closed under arbitrary intersections when M has finite diameter.

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