The Radon-Nikodym theorem for Lebesgue-Bochner function spaces

The near Radon-nikodym Property in Lebesgue-bochner Function Spaces

Let X be a Banach space and (Ω,Σ, λ) be a finite measure space, 1 ≤ p < ∞. It is shown that L(λ,X) has the Near Radon-Nikodym property if and only if X has it. Similarly if E is a Köthe function space that does not contain a copy of c0, then E(X) has the Near Radon-Nikodym property if and only if X does.

The Radon-Nikodym Theorem for Reflexive Banach Spaces El Teorema de Radon-Nikodym para Espacios de Banach Reflexivos

In this short paper we prove the equivalence between the RadonNikodym Theorem for reflexive Banach spaces and the representability of weakly compact operators with domain L(μ).

Extreme points of the unit cell Lebesgue-Bochner function spaces

A Reformulation of the Radon-nikodym Theorem

The Radon-Nikodym theorems of Segal and Zaanen are principally concerned with the classification of those measures p. for which any X« p. is given in the form

Strong Barrelledness Properties in Lebesgue-Bochner Spaces

If (Ω,Σ, μ) is a finite atomless measure space and X is a normed space, we prove that the space Lp(μ,X), 1 ≤ p ≤ ∞ is a barrelled space of class א0, regardless of the barrelledness of X. That enables us to obtain a localization theorem of certain mappings defined in Lp(μ,X). By “space” we mean a “real or complex Hausdorff locally convex space”. Given a dual pair (E,F ), as usual σ(E,F ) denotes...