Szlenk indices and uniform homeomorphisms

DOI10.1090/S0002-9947-01-02825-2zbMath0981.46007arXivmath/9911017OpenAlexW2592942135MaRDI QIDQ2723456

Gilles Godefroy, Nigel J. Kalton, Gilles Lancien

Publication date: 5 July 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9911017

zbMATH Keywords

Szlenk indexuniform homeomorphismsnon reflexive Banach spacesUKK\(^{\ast }\)-renorminguniform Kadec-Klee renorming

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isomorphic theory (including renorming) of Banach spaces (46B03)

Related Items (45)

Smoothness, asymptotic smoothness and the Blum-Hanson property ⋮ Power type asymptotically uniformly smooth and asymptotically uniformly flat norms ⋮ Direct sums and summability of the Szlenk index ⋮ Asymptotic geometry of Banach spaces and uniform quotient maps ⋮ Operators on $C(K)$ spaces preserving copies of Schreier spaces ⋮ Szlenk indices of convex hulls ⋮ Obituary: Nigel John Kalton, 1946-2010 ⋮ Nonlinear equivalence of Banach spaces based on Birkhoff-James orthogonality. II ⋮ Higher projective tensor products of $c_0$ ⋮ A note on the relationship between the Szlenk and \(w^*\)-dentability indices of arbitrary \(w^*\)-compact sets ⋮ On Kalton’s interlaced graphs and nonlinear embeddings into dual Banach spaces ⋮ Non-three space properties and Szlenk index ⋮ The isomorphism class of \(c_0\) is not Borel ⋮ Asymptotic smoothness and universality in Banach spaces ⋮ The Szlenk power type and tensor products of Banach spaces ⋮ Compact spaces of Szlenk index \(\omega\) ⋮ The universality of \(\ell _{1}\) as a dual space ⋮ \(\xi\)-asymptotically uniformly smooth, \(\xi\)-asymptotically uniformly convex, and (\(\beta\)) operators ⋮ Unnamed Item ⋮ Examples of uniformly homeomorphic Banach spaces ⋮ Separated sets and Auerbach systems in Banach spaces ⋮ Operator ideals and three-space properties of asymptotic ideal seminorms ⋮ COMPARING THE GENERALISED ROUNDNESS OF METRIC SPACES ⋮ The non-linear geometry of Banach spaces after Nigel Kalton ⋮ Equivalent norms with the property \((\beta)\) of Rolewicz ⋮ Power type $\xi $-asymptotically uniformly smooth norms ⋮ Power type \(\xi\)-asymptotically uniformly smooth and \(\xi\)-asymptotically uniformly flat norms ⋮ The Szlenk index of Orlicz sequence spaces ⋮ Uniform homeomorphisms of Banach spaces and asymptotic structure ⋮ The coarse Lipschitz geometry of \(\ell_p\oplus\ell_q\) ⋮ The uniform structure of Banach spaces ⋮ Analytic sets of Banach spaces ⋮ Uniformly convex renormings and generalized cotypes ⋮ Twisted sums with 𝐶(𝐾) spaces ⋮ The transfer of property $(\beta )$ of Rolewicz by a uniform quotient map ⋮ CONCERNING SUMMABLE SZLENK INDEX ⋮ Tsirelson-like spaces and complexity of classes of Banach spaces ⋮ Three and a half asymptotic properties ⋮ Automorphisms of \(\mathcal C(K)\)-spaces and extension of linear operators ⋮ Prescribed Szlenk index of separable Banach spaces ⋮ The dual of the Bourgain-Delbaen space ⋮ Constructing a Lipschitz retraction from ℬ(ℋ) onto 𝒦(ℋ) ⋮ An asymptotic property of Schachermayer's space under renorming ⋮ Finite slicing in superreflexive Banach spaces ⋮ Asymptotic smoothness in Banach spaces, three-space properties and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence of separable uniformly homeomorphic nonisomorphic Banach spaces
• A double-dual characterization of separable Banach spaces containing \(\ell^1\)
• Martingales with values in uniformly convex spaces
• On asymptotic structure, the Szlenk index and UKK properties in Banach spaces
• The uniform nonequivalence of \(L_ p\) and \(\ell_ p\)
• The dual of the Bourgain-Delbaen space
• Subspaces of \(c_0 (\mathbb{N})\) and Lipschitz isomorphisms
• Banach spaces determined by their uniform structures
• The Szlenk index and local \(\ell_1\)-indices
• Banach spaces whose duals are isomorphic to \(l_1(\Gamma)\)
• Banach spaces which can be given an equivalent uniformly convex norm
• ALMOST FRÉCHET DIFFERENTIABILITY OF LIPSCHITZ MAPPINGS BETWEEN INFINITE-DIMENSIONAL BANACH SPACES
• L'espace de Banach C0 est déterminé par sa métrique
• Distances between Banach spaces
• Property (M), M-ideals, and almost isometric structure of Banach spaces.
• Subspaces of the Bourgain-Delbaen space
• Applications of ultrapowers to the uniform and Lipschitz classification of Banach spaces
• The non-existence of a separable reflexive Banach space universal for all separable reflexive Banach spaces

This page was built for publication: Szlenk indices and uniform homeomorphisms