Topological open problems in the geometry of Banach spaces.
On Compactness in Locally Convex Spaces.
Projetive generators and resolutions of identity in Banach spaces.
We introduce the notion of projective generator on a given Banach space. Weakly countably determined and dual spaces with the Radon Nikodým property have projective generators. If a Banach space has projective generator, then it admits a projective resolution of the identity. When a Banach space and its dual both have a projective generator then the space admits a shrinking resolution of the identity. These results include previous ones of Amir and Lindenstrauss, John and Zizler, Gul?ko, Vaak, Tacon,...
LUR renormings through Deville's Master Lemma.
Every Radon-Nikodym Corson compact space is Eberlein compact
The Lindelöf property in Banach spaces
A topological space (T,τ) is said to be fragmented by a metric d on T if each non-empty subset of T has non-empty relatively open subsets of arbitrarily small d-diameter. The basic theorem of the present paper is the following. Let (M,ϱ) be a metric space with ϱ bounded and let D be an arbitrary index set. Then for a compact subset K of the product space the following four conditions are equivalent: (i) K is fragmented by , where, for each S ⊂ D, . (ii) For each countable subset A of D, is...
James boundaries and σ-fragmented selectors
We study the boundary structure for w*-compact subsets of dual Banach spaces. To be more precise, for a Banach space X, 0 < ϵ < 1 and a subset T of the dual space X* such that ⋃ B(t,ϵ): t ∈ T contains a James boundary for we study different kinds of conditions on T, besides T being countable, which ensure that . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if is the duality mapping and there exists a σ-fragmented map f: X → X* such that B(f(x),ϵ)...
Countably determined locally convex spaces
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