E. A. Sánchez Pérez

Generalized perfect spaces

Abstract Given two Banach function spaces X and Y related to a measure μ, the Y-dual space XY of X is defined as the space of the multipliers from X to Y. The space XY is a generalization of the classical Kothe dual space of X, which is obtained by taking Y = Lt(μ). Under minimal conditions, we can consider the Y-bidual space XYY of X (i.e. the Y-dual of XY). As in the classical case, the containment X ⊂ XYY always holds. We give conditions guaranteeing that X coincides with XYY, in which case X is said to be Y-perfect. We also study when X is isometrically embedded in XYY. Properties involving p-convexity, p-concavity and the order of X and Y, will have a special relevance.

Factorization of strongly (p, σ)-continuous multilinear operators

We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal – which is also new for the linear case – is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.

Dominated extensions of functionals and V -convex functions of cancellative cones

Let C be a cancellative cone and consider a subcone Co of C. We study the natural problem of obtaining conditions on a non negative homogeneous function : C -> R + so that for each linear functional / defined in Co which is bounded by , there exists a linear extension to C In order to do this we assume several geometric conditions for cones related to the existence of special algebraic basis of the linear span of these cones.

The associated tensor norm to (q,p)-absolutely summing operators on C(K)-Spaces

AbstractWe give an explicit description of a tensor norm equivalent on

Optimal Extensions for pth Power Factorable Operators

C(K){\text{ }} \otimes {\text{ }}F

Vector valued information measures and integration with respect to fuzzy vector capacities

to the associated tensor norm νqp to the ideal of (g,p)-absolutely summing operators. As a consequence, we describe a tensor norm on the class of Banach spaces which is equivalent to the left projective tensor norm associated to νqp.

Topological Dual Systems for Spaces of Vector Measure -Integrable Functions

Abstract Given a set function Λ with values in a Banach space X, we construct an integration theory for scalar functions with respect to Λ by using duality on X and Choquet scalar integrals. Our construction extends the classical Bartle–Dunford–Schwartz integration for vector measures. Since just the minimal necessary conditions on Λ are required, several L 1 -spaces of integrable functions associated to Λ appear in such a way that the integration map can be defined in them. We study the properties of these spaces and how they are related. We show that the behavior of the L 1 -spaces and the integration map can be improved in the case when X is an order continuous Banach lattice, providing new tools for (non-linear) operator theory and information sciences.

Lattice Copies of ℓ2 in L1 of a Vector Measure and Strongly Orthogonal Sequences

Let