The approximation property for spaces of Lipschitz functions

Abstract

Let $\mathrm{Lip}_0(X)$ be the space of all Lipschitz scalar-valued functions on a pointed metric space $X$. We characterize the approximation property for $\mathrm{Lip}_0(X)$ with the bounded weak* topology using as tools the tensor product, the $\epsilon$-product and the linearization of Lipschitz mappings.