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arXiv · 1703.07896

Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete

Tomasz Kochanek·Eva Pernecká
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Abstract

Let $M$ be a compact subset of a superreflexive Banach space. We prove that the Lipschitz-free space $\mathcal{F}(M)$, the predual of the Banach space of Lipschitz functions on $M$, has the Pe{\l}czy\'nski's property ($V^\ast$). As a consequence, the Lipschitz-free space $\mathcal{F}(M)$ is weakly sequentially complete.

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Tomasz Kochanek, Eva Pernecká. 2017-03-23. Lipschitz-free spaces over compact subsets of superreflexive spaces are weakly sequentially complete. https://doi.org/10.1112/blms.12179

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