SUBSPACES OF c 0 ( N ) AND LIPSCHITZ ISOMORPHISMS
نویسنده
چکیده
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 the dual unit sphere. Estimates on the Banach–Mazur distances are provided when the Lipschitz constants of the isomorphisms are small. The quite different non-separable theory is also investigated.
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