Banach spaces and bilipschitz maps
We show that a normed space E is a Banach space if and only if there is no bilipschitz map of E onto E ∖ {0}.
Banach spaces and large cardinals
Banach spaces and operators which are nearly uniformly convex [Book]
Banach Spaces Determined by Their Uniform Structures.
Banach spaces in which all multilinear forms are weakly sequentially continuous
We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an...
Banach spaces isomorphic to proper M-ideals
Banach spaces not having copies of 1 ∞ and Z1.
Banach spaces of bounded Szlenk index
For a countable ordinal α we denote by the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each admits a separable, reflexive universal space. We also show that spaces in the class embed into spaces of the same class with a basis. As a consequence we deduce that each is analytic in the Effros-Borel structure of subspaces of C[0,1].
Banach spaces of bounded Szlenk index II
For every α < ω₁ we establish the existence of a separable Banach space whose Szlenk index is and which is universal for all separable Banach spaces whose Szlenk index does not exceed . In order to prove that result we provide an intrinsic characterization of which Banach spaces embed into a space admitting an FDD with Tsirelson type upper estimates.
Banach Spaces of Compact Multipliers and Their Dual Spaces.
Banach spaces of functions analytic in a polydisc.
Banach spaces of homogeneous polynomials without the approximation property
We present simple proofs that spaces of homogeneous polynomials on and provide plenty of natural examples of Banach spaces without the approximation property. By giving necessary and sufficient conditions, our results bring to completion, at least for an important collection of Banach spaces, a circle of results begun in 1976 by R. Aron and M. Schottenloher (1976).
Banach spaces of Lipschitz functions
Banach Spaces of Locally Schlicht Functions with the Hornich Operations.
Banach Spaces of Solutions of the Hemholtz Equation in the Plane.
Banach Spaces of Type p have Arbitrarily Distortable Subspaces.
Banach spaces on which every unconditionally converging operator is completely continuous
Banach spaces quasi-reflexive of order one
Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. Part II.
Banach spaces which admit a norm with the uniform Kadec-Klee property
Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.