We show that the class of subspaces of c0(N) is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz-isomorphic to c0(N) is linearly isomorphic to c0(N). The proof relies in part on an isomorphic characterization of subspaces of c0(N) as separable spaces having an equivalent norm such that the weak-star and norm topologies quantitatively agree on t...

We provide a generalization of a well known Krasnosel’skii theorem on continuity of the Nemytskii operator for functions taking values in separable Banach spaces. We follow the results obtained in [6] for the finite dimensional case.

We prove that every Banach space containing a complemented copy of c0 has an antiproximinal body for a suitable norm. If, in addition, the space is separable, there is a pair of antiproximinal norms. In particular, in a separable polyhedral space X, the set of all (equivalent) norms on X having an isomorphic antiproximinal norm is dense. In contrast, it is shown that there are no antiproximinal...