Resumen de The approximation property for spaces of Lipschitz functions with the bounded weak* topology
Let X be a pointed metric space and let Lip0(X) be the space of all scalar-valued Lipschitz functions on X which vanish at the base point. We prove that Lip0(X) with the bounded weak* topology τbw∗ has the approximation property if and only if the Lipschitz-free Banach space F(X) has the approximation property if and only if, for each Banach space F, each Lipschitz operator from X into F can be approximated by Lipschitz finite-rank operators within the unique locally convex topology γτγ on Lip0(X,F) such that the Lipschitz transpose mapping f↦ft is a topological isomorphism from Lip0(X,F),γτγ) to (Lip0(X),τbw∗)ϵF.
