O. Delgado

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.

Banach function subspaces of L1 of a vector measure and related Orlicz spaces

Abstract Given a vector measure ν with values in a Banach space X, we consider the space L1(ν) of real functions which are integrable with respect to ν. We prove that every order continuous Banach function space Y continuously contained in L1(ν) is generated via a certain positive map ϱ related to ν and defined on X* x M, where X* is the dual space of X and M the space of measurable functions. This procedure provides a way of defining Orlicz spaces with respect to the vector measure ν.

Choquet type L 1 -spaces of a vector capacity

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.

Optimal Extensions for pth Power Factorable Operators

Let

Optimal domain for the Hardy operator

{X(\mu)}

On the Banach lattice structure of L^1_w of a vector measure on a \delta -ring

X(μ) be a function space related to a measure space

Optimal Domains for L0-valued Operators Via Stochastic Measures

{(\Omega,\Sigma,\mu)}