Abstract of a paper by Colin Petitjean, Antonín Procházka
This is an announcement for the paper “On exposed points of Lipschitz free spaces” by Colin Petitjean<https://arxiv.org/search/math?searchtype=author&query=Petitjean%2C+C>, Antonín Procházka<https://arxiv.org/search/math?searchtype=author&query=Proch%C3%A1zka%2C+A>. 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 $[x,y]=\{z \in M \; : \; d(x,y)=d(z,x)+d(z,y) \}$ 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. The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1810.12031
participants (1)
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Bentuo Zheng (bzheng)