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

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 Pełczyński's property ($V^{\ast }$). As a consequence, the Lipschitz-free space $\mathcal{F}(M)$ is weakly sequentially complete.

19 pages. Section 4 providing examples added. Connections between the main result and properties (V*) and (X) discussed in the Introduction