Weakly compact composition operators on spaces of Lipschitz functions

Abstract

Let $X$ be a pointed compact metric space. Assuming that ${\mathrm{lip}}_0(X)$ has the uniform separation property, we prove that every weakly compact composition operator on spaces of Lipschitz functions ${\mathrm{Lip}}_0(X)$ and ${\mathrm{lip}}_0(X)$ is compact.

6 pages