The distortion problem

DOI10.1007/BF02398436zbMath0828.46005arXivmath/9607207OpenAlexW2055731028MaRDI QIDQ1343834

Edward Odell, Thomas Schlumprecht

Publication date: 11 January 1996

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9607207

zbMATH Keywords

equivalent normuniform homeomorphismdistortable Banach spacedistorted normgeneral distortion problem

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Classical Banach spaces in the general theory (46B25) Isomorphic theory (including renorming) of Banach spaces (46B03)

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Cites Work

• Espaces de Banach superstables, distances stables et homeomorphismes uniformes
• Existence of separable uniformly homeomorphic nonisomorphic Banach spaces
• Asymptotic theory of finite dimensional normed spaces. With an appendix by M. Gromov: Isoperimetric inequalities in Riemannian manifolds
• Lipschitz functions on classical spaces
• An arbitrarily distortable Banach space
• A nonreflexive Banach space that is uniformly nonoctahedral
• Not every Banach space contains an imbedding of \(l_p\) or \(c_0\)
• Geometry of Banach spaces. Selected topics
• Sous-espaces de dimension finie des espaces de Banach reticules
• On uniform homeomorphisms of the unit spheres of certain Banach lattices
• Uniformly non-square Banach spaces
• Isomorphous Banach structures
• On a problem of Smirnov
• Contributions to the theory of the classical Banach spaces
• The Unconditional Basic Sequence Problem
• Differentials of Complex Interpolation Processes for Kothe Function Spaces
• A Characterization of Banach Spaces Containing l ¹
• Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach
• Normalized weakly null sequence with no unconditional subsequence
• GEOMETRIC THEORY OF BANACH SPACES. PART II. GEOMETRY OF THE UNIT SPHERE
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