Francisco Naranjo

Antonio Fernández; Francisco Naranjo

Abstract For a real Frechet space X with dual X′ the following conditions are equivalent: 1. (a) X admits a continuous norm. 2. (b) Every convex and weakly compact subset of X is the closed convex hull of its exposed points. 3. (c) For every X-valued, countably additive measure ν there exists x′ in X′ such that ν is ¦x′ v¦- continuous .

Antonio Fernández; Fernando Mayoral; Francisco Naranjo; Enrique A. Sánchez-Pérez

Let (Ω, Σ) be a measurable space andm: Σ →X be a vector measure with values in the complex Banach space X: We apply the Calderón interpolation methods to the family of spaces of scalarp-integrable functions with respect tom with 1≤p≤∞. Moreover we obtain a result about the relation between the complex interpolation spaces [X0,X1][θ] and [X0,X1][θ] for a Banach couple of interpolation (X0,X1) such thatX1 ⊂X0 with continuous inclusion.

Antonio Fernández; Francisco Naranjo

We study the question of determining conditions for the space of R-valued integrable functions with respect to a vector measure taking its values in a real Fréchet space to be an AL- or an AM-space.

Ricardo del Campo; Antonio Fernández; Fernando Mayoral; Francisco Naranjo; Irene Ferrando

We study properties of compactness of multiplication operators between spaces of p-power integrable scalar functions with respect to a vector measure m.

Antonio Fernández; Fernando Mayoral; Francisco Naranjo; José Manuel Rodríguez

Abstract Let v be a countably additive measure defined on a measurable space (Ω, Σ) and taking values in a Banach space X. Let f : Ω → ℝ be a measurable function. In order to check the integrability (respectively, weak integrability) of f with respect to v it is sometimes enough to test on a norming set Λ ⊂ X*. In this paper we show that this is the case when A is a James boundary for B X * (respectively, Λ is weak*-thick). Some examples and applications are given as well.

Antonio Fernández; Francisco Naranjo

We consider the space L 1 (ν, X ) of all real functions that are integrable with respect to a measure v with values in a real Frechet space X . We study L-weak compactness in this space. We consider the problem of the relationship between the existence of copies of l ∞ in the space of all linear continuous operators from a complete DF-space Y to a Frechet lattice E with the Lebesgue property and the coincidence of this space with some ideal of compact operators. We give sufficient conditions on the measure ν and the space X that imply that L 1 (ν, X ) has the Dunford-Pettis property. Applications of these results to Frechet AL-spaces and Kothe sequence spaces are also given.

Antonio Fernández; Francisco Naranjo

Abstract For Frechet lattices with the Lebesgue property and weak order unit we prove that the following conditions are equivalent: 1. (1) there exists a strictly positive linear functional, 2. (2) the Frechet lattice admits a continuous norm. In this setting we obtain a representation theorem for Frechet lattices.

Antonia Fernández; Fernando Mayoral; Francisco Naranjo; C. Sáez; Enrigue A. Sánchez-Pérez

Antonio Fernández; Fernando Mayoral; Francisco Naranjo; C. Sáez; Enrique A. Sánchez-Pérez

Antonio Fernández; Fernando Mayoral; Francisco Naranjo; C. Sáez; Enrique A. Sánchez-Pérez