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

## TL;DR

This paper proves that Lipschitz-free spaces over compact subsets of superreflexive Banach spaces are weakly sequentially complete, advancing understanding of their structural properties.

## Contribution

It establishes that such Lipschitz-free spaces have Pe{{}czyski's property ($V^*$), a significant structural result.

## Key findings

- Lipschitz-free spaces over compact subsets of superreflexive spaces have property ($V^*$)
- These spaces are weakly sequentially complete
- Advances understanding of the structure of Lipschitz-free spaces

## 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.