Currently displaying 1 – 8 of 8

Showing per page

Order by Relevance | Title | Year of publication

Projetive generators and resolutions of identity in Banach spaces.

J. OrihuelaM. Valdivia — 1989

Revista Matemática de la Universidad Complutense de Madrid

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,...

The Lindelöf property in Banach spaces

B. CascalesI. NamiokaJ. Orihuela — 2003

Studia Mathematica

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 M D the following four conditions are equivalent: (i) K is fragmented by d D , where, for each S ⊂ D, d S ( x , y ) = s u p ϱ ( x ( t ) , y ( t ) ) : t S . (ii) For each countable subset A of D, ( K , d A ) is...

James boundaries and σ-fragmented selectors

B. CascalesM. MuñozJ. Orihuela — 2008

Studia Mathematica

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 B X * we study different kinds of conditions on T, besides T being countable, which ensure that X * = s p a n T ¯ | | · | | . (SP) We analyze two different non-separable cases where the equality (SP) holds: (a) if J : X 2 B X * is the duality mapping and there exists a σ-fragmented map f: X → X* such that B(f(x),ϵ)...

Page 1

Download Results (CSV)