SUBSPACES OF c0(IN) AND LIPSCHITZ ISOMORPHISMS

We show that the class of subspaces of c0(IN) is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz-isomorphic to c0(IN) is linearly isomorphic to c0(IN). The proof relies in part on an isomorphic characterization of subspaces of c0(IN) as separable spaces having an equivalent norm with a quantitative form of the weak-star Kadec-Klee property. Quantitative results are shown when the Lipschitz constants of the isomorphisms are small. The quite different non separable theory is also investigated. 1