Jiménez Fernández, Eduardo; Juan Blanco, María Aránzazu; Sánchez Pérez, Enrique Alfonso(Elsevier, 2011)
Consider a Banach function space X(mu) of (classes of) locally integrable functions over a sigma-finite measure space (Omega, Sigma, mu) with the weak sigma-Fatou property. Day and Lennard (2010) [9] proved that the theorem ...
We introduce the new class of the (p;p1,...,pm; s)-absolutely continuous operators, that is defined using a summability property that provides the multilinear version of the (p, s)-absolutely continuous operators. We give ...
[EN] We prove that, under some reasonable requirements, the unit balls of the spaces Lp(m) and Loo(m) of a vector measure of compact range m are compact with respect to the topology t_m of pointwise convergence of the ...
El presente trabajo está dedicado al análisis de una clase particular de operadores (lineales
y continuos) entre espacios de Banach de funciones. El objetivo es avanzar en la teoría de
los llamados operadores factorizables ...
[EN] In this paper, we characterize compact linear operators from
Banach function spaces to Banach spaces by means of approximations
with bounded homogeneous maps. To do so, we undertake a detailed
study of such maps, ...
Consider an operator T : X--->Y between Banach function
spaces having adequate order continuity and Fatou properties.
Assume that T can be factorized through a Banach space as T =SR,
where R and the adjoint of S are ...
Del Campo Acosta, Ricardo; Fernández Carrión, Antonio; Mayoral, Fernando; Naranjo, Francisco; Sánchez Pérez, Enrique Alfonso(Springer Verlag, 2011)
[EN] Let (Omega, Sigma) be a measurable space and m(0) : Sigma -> X-0 and m(1) : Sigma -> X-1 be positive vector measures with values in the Banach Kothe function spaces X-0 and X-1. If 0 < alpha < 1, we define a new vector ...
[EN] Let m be a Banach space valued measure. We study some domination
properties of the integration operator that are equivalent to the existence
of Banach ideals of L1(m) that are interpolation spaces. These ...
Calabuig, J. M.; Jiménez Fernández, Eduardo; Juan Blanco, María Aránzazu; Sánchez Pérez, Enrique Alfonso(Elsevier, 2016)
[EN] Compactness type properties for operators acting in Banach function spaces are not always preserved when the operator is extended to a bigger space. Moreover, it is known that there exists a maximal (weakly) compact ...
[EN] Consider an operator T : E → X(µ) from a Banach space E to
a Banach function space X(µ) over a finite measure µ such that its dual map
is p-th power factorable. We compute the optimal range of T that is defined
to ...
[EN] 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 ...
[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake
an analysis of the supports of non-zero functions in strongly embedded subspaces of
Banach functions spaces. The main aim is to ...
Let X(mu) be a Banach function space. In this paper we introduce two new geometric notions, q-convexity and weak q-convexity associated to a subset S of the unit ball of the dual of X(mu), 1 = q < 8. We prove that in the ...
[EN] An explicit construction for the representation of the Calderón interpolation of spaces of vector measure integrable functions is given as well as for the representation of the real interpolation of these spaces using ...