Banach spaces all of whose subspaces have the approximation property
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 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 Type p have Arbitrarily Distortable Subspaces.
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.
Banach spaces which are -ideals in their bidual have property
We show that every Banach space which is an -ideal in its bidual has the property of Pelczynski. Several consequences are mentioned.
Banach spaces which are proper M-ideals
Banach spaces which are semi-L-summands in their biduals.
Banach spaces which embed into their dual
We use Birkhoff-James' orthogonality in Banach spaces to provide new conditions for the converse of the classical Riesz representation theorem.
Banach spaces whose bounded sets are bounding in the bidual.
Banach Spaces with the Condition of Mazur.
Banach-Mazur distance of central sections of a centrally symmetric convex body.
Banach-Mazur Distances and Projections on p-convex Spaces.
Banach-Saks property in some Banach sequence spaces
It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.
Banach-Stone theorems for non-separably valued Bochner – spaces
Bi-Lipschitz embeddings of hyperspaces of compact sets
We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the...