Gilles Lancien

Szlenk indices and uniform homeomorphisms

We prove some rather precise renorming theorems for Banach spaces with Szlenk index wo. We use these theorems to show the invariance of certain quantitative Szlenk-type indices under uniform homeomorphisms.

Subspaces of

Abstract. We show that the class of subspaces of

c_0 ({\Bbb N})

c_0 ({\Bbb N})

and Lipschitz isomorphisms

is stable under Lipschitz isomorphisms. The main corollary is that any Banach space which is Lipschitz-isomorphic to

A NEW METRIC INVARIANT FOR BANACH SPACES

c_0 ({\Bbb N})

The non-linear geometry of Banach spaces after Nigel Kalton

is linearly isomorphic to

Embeddings of locally finite metric spaces into Banach spaces

c_0 ({\Bbb N})

Asymptotic geometry of Banach spaces and uniform quotient maps

. The proof relies in part on an isomorphic characterization of subspaces of

Universality of Asplund spaces

c_0 ({\Bbb N})

Weak* dentability index of spaces C([0,α])

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.