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 ...
Agud Albesa, Lucia; Calabuig, J. M.; Juan, Maria Aranzazu; Sánchez Pérez, Enrique Alfonso(MDPI AG, 2020-01)
[EN] Let (Omega,sigma,mu) be a finite measure space and consider a Banach function space Y(mu). We say that a Banach space E is representable by Y(mu) if there is a continuous bijection I:Y(mu)-> E. In this case, it is ...
[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 ...
Calabuig, J. M.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, Enrique Alfonso(Springer-Verlag, 2019-10)
[EN] Given s-finite measure spaces ( 1, 1, mu 1) and ( 2, 2, mu 2), we consider Banach spaces X1(mu 1) and X2(mu 2), consisting of L0(mu 1) and L0(mu 2) measurable functions respectively, and study when the completion of ...
Agud Albesa, Lucia; Calabuig, J. M.; Lajara, Sebastian; Sánchez Pérez, Enrique Alfonso(Springer-Verlag, 2017-07)
[EN] We study the properties of Gâteaux, Fréchet, uniformly Fréchet and uniformly Gâteaux smoothness of the space Lp(m) of scalar p-integrable functions with respect to a positive vector measure m with values in a Banach ...
Galdames Bravo, Orlando Eduardo(Universitat Politècnica de València, 2013-07-29)
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 ...
Calabuig, J. M.; Fernández-Unzueta, Maite; Galaz-Fontes, Fernando; Sánchez Pérez, Enrique Alfonso(The Korean Mathematical Society, 2019-09)
[EN] Consider a finite measure space (Omega, Sigma, mu) and a Banach space X(mu) consisting of (equivalence classes of) real measurable functions defined on Omega such that f chi(A) is an element of X(mu) and parallel to ...
[EN] Let X be a saturated Banach function space and denote by X' its Kothe dual. In the paper (Delgado and Sanchez Perez in Positivity 20: 999-1014, 2016) referenced in the title it is implicitly used that the closed unit ...
Calabuig, J. M.; Rodríguez, José; Sánchez Pérez, Enrique Alfonso(Cambridge University Press, 2017-12)
[EN] We analyze domination properties and factorization of operators in Banach spaces through subspaces of L1-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we ...
[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 ...
del Campo, R.; Fernández, A.; Mayoral, F.; Naranjo, F.; Sánchez Pérez, Enrique Alfonso(Informa UK (National Inquiry Services Center), 2020-08-03)
[EN] 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 ...
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] We explore the connection between p-regular operators on Banach function spaces and weighted p-estimates. In particular, our results focus on the following problem. Given finite measure spaces mu and nu, let T be an ...
[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 ...