On exposed points of Lipschitz free spaces

Abstract

In this note we prove that a molecule $d(x,y{)}^{-1}(\delta (x)-\delta (y))$ is an exposed point of the unit ball of a Lispchitz free space $\mathcal{F}(M)$ if and only if the metric segment $[x,y]=\{z\in M:d(x,y)=d(z,x)+d(z,y)\}$ 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.

References in corpus (1)

• On the preserved extremal structure of Lipschitz-free spaces