SÁNCHEZ PÉREZ , E. A.

Let T : X1 → Y1 and S : X2 → Y2 be two continuous linear operators between Banach function spaces related to a finite measure space. Under some lattice requirements on the spaces involved, we give characterizations by means of inequalities of when T can be strongly factorized through S, that is, T = Mg ◦ S ◦Mf with Mf : X1 → X2 and Mg : Y2 → Y1...

Consider a couple of Banach function spaces X and Y over the same measure space and the space XY of multiplication operators from X into Y . In this paper we develop the setting for characterizing certain summability properties satisfied by the elements of XY . At this end, using the "generalized K¨othe duality" for Banach function spaces, we...

Let X be a saturated Banach function space and denote by X′ its Köthe dual. In the paper (Delgado and Sánchez Pérez in Positivity 20:999–1014, 2016) referenced in the title it is implicitly used that the closed unit ball BX′ of X′ is compact for the topology σ(X′,X) on X′ defined by the elements of X. This fact could be not true in general if X...

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,...

Given a Banach space valued q-concave linear operator T defined on a σ-order continuous quasi-Banach function space, we provide a description of the optimal domain of T preserving q-concavity, that is, the largest σ-order continuous quasi-Banach function space to which T can be extended as a q-concave operator. We show in this way the existence...

Let X(μ) be a function space related to a measure space (Ω,Σ, μ) with χΩ ∈ X(μ) and let T : X(μ) → E be a Banach spacevalued operator. It is known that if T is pth power factorable then the largest function space to which T can be extended preserving pth power factorability is given by the space Lp(mT) of p-integrable functions with respect to...

Consider two continuous linear operators T : X1(μ) ! Y1( ) and S : X2(μ) ! Y2( ) between Banach function spaces related to different -finite measures μ and . We characterize by means of weighted norm inequalities when T can be strongly factored through S, that is, when there exist functions g and h such that T (f) = gS(hf) for all f 2...

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 Köthe 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...

In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz...

We study some Banach lattice properties of the space L1 w(ν) of weakly integrable functions with respect to a vector measure ν defined on a δ-ring. Namely, we analyze order continuity, order density and Fatou type properties. We will see that the behavior of L1 w(ν) differs from the case in which ν is defined on a σ -algebra whenever ν does not...