On the structure of Lipschitz-free spaces (Q2814404)

This article investigates the structure of Lipschitz free spaces over metric spaces \(M\), that is, of natural preduals of the space of real-valued Lipschitz functions over a metric space \(M\). This class of Banach spaces, which are separable if \(M\) is and are easy to define, is still poorly understood although it has attracted a lot of attention in the last fifteen years. The present work establishes several nice properties of the free spaces over specific metric spaces. It is shown for instance that there exists a compact metric space which is actually a convergent sequence \(S\), such that the free space over \(S\) does not isomorphically embed into \(L_1\). Another interesting result is that if \(M\) is a subset of a finite-dimensional normed space, then the free space over \(M\) is weakly sequentially complete. Commented open problems conclude this interesting article.