Abstract:
Let M be a pointed metric space and Lip0 (M ) the space of Lipschitz functions vanishing at 0. Endowed with the Lipschitz norm this space is a Banach space. Denote F(M ) the closed subspace of Lip(M )* spanned by the evaluation points and call it the Lipschitz-free space over M.
After an introduction explaining how one can use these spaces in the context of non linear classification of Banach spaces, we will more particularly be interested in dual Lipschitz-free spaces and shortly explain there link with optimal transportation.