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Artículo
Strong Factorizations between Couples of Operators on Banach Function Spaces
(Heldermann Verlag, 2013)
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 ...
Artículo
Orlicz spaces associated to a quasi‑Banach function space: applications to vector measures and interpolation
(Springer, 2021)
The Orlicz spaces XΦ associated to a quasi-Banach function space X are defined by replacing the role of the space L1 by X in the classical construction of Orlicz spaces. Given a vector measure m, we can apply this ...
Artículo
Complex Interpolation of Operators and Optimal Domains
(Springer, 2014)
Let X0 and X1 be two order continuous Banach function spaces on a finite measure space, (E0, E1) a Banach space interpolation pair, and T : X0 + X1 → E0 + E1 an admissible operator between the pairs (X0, X1) and (E0, ...
Artículo
Factorizing operators on Banach function spaces through spaces of multiplication operators
(Elsevier, 2010)
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 ...
Artículo
The space of scalarly integrable functions for a Fréchet-space-valued measure
(Elsevier, 2009)
The space L1 w (ν) of all scalarly integrable functions with respect to a Fréchet-space-valued vector measure ν is shown to be a complete Fréchet lattice with the σ-Fatou property which contains the (traditional) space ...
Artículo
Compactness in quasi-Banach function spaces with applications to L1 of the semivariation of a vector measure
(Springer, 2020)
We characterize the relatively compact subsets of the order continuous part Ea of a quasi Banach function space E showing that the strong connection between compactness, uniform absolute continuity, uniform integrability, ...
Artículo
When and where the Orlicz and Luxemburg (quasi-) norms are equivalent?
(Elsevier, 2020)
We study the equivalence between the Orlicz and Luxemburg (quasi-) norms in the context of the generalized Orlicz spaces associated to an N-function Φ and a (quasi-) Banach function space X over a positive finite measure ...
Artículo
Optimal Domains for L0-valued Operators Via Stochastic Measures
(Springer, 2007)
We study extension of operators T : E → L0([0, 1]), where E is an F–function space and L0([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the ...
Artículo
Lorentz spaces of vector measures and real interpolation of operators
(Taylor and Francis, 2020)
Using the representation of the real interpolation of spaces of p-integrable functions with respect to a vector measure, we show new factorization theorems for p th power factorable operators acting in interpolation couples ...
Artículo
Interpolation of Vector Measures
(Springer, 2011)
Let (Ω, Σ) be a measurable space and m 0: Σ → X 0 and m 1: Σ → X 1 be positive vector measures with values in the Banach Köthe function spaces X 0 and X 1. If 0 < α < 1, we define a new vector measure [m 0, m 1] α with ...