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 present a characterization of Banach function lattices with the Fatou property
generated by the interpolation sum applied to infinite families of Banach lattices with the Fatou
property. We also discuss the Köthe ...
Calabuig Rodriguez, Jose Manuel; Lajara, S.; Rodríguez Ruiz, José; Sánchez Pérez, Enrique Alfonso(Polskiej Akademii Nauk, Instytut Matematyczny (Polish Academy of Sciences, Institute of Mathematics), 2014)
We study compactness and related topological properties in the space
L1(m) of a Banach space valued measure m when the natural topologies associated to convergence of vector valued integrals are considered. The resulting ...
[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.; 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 ...
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 ...
We study the Kothe dual spaces of Banach function lattices generated by abstract methods having roots in the theory of interpolation spaces. We apply these results to Banach spaces of integrable functions with respect to ...
Okada, S.; Ricker, W. J.; Sánchez Pérez, Enrique Alfonso(Polish Academy od Sciences. Institute of Matematics, 2014)
The spaces L1(m) of all m-integrable (resp. L1w(m) of all scalarly m-integrable) functions for a
vector measure m, taking values in a complex locally convex Hausdorff space X (briefly, lcHs),
are themselves lcHs for the ...
Let m be an l(2)-valued (countably additive) vector measure and consider the space L-2(m) of square integrable functions with respect to m. The integral with respect to m allows to define several notions of orthogonal ...
[EN] A subset B of a set-algebra A has property N if each B-pointwise bounded subset M of bounded measures of bounded variation is A -uniformly bounded. Each σ-algebra has property N and there exists algebras which ...
We investigate natural sufficient conditions for a space L p(m) of pintegrable functions with respect to a positive vector measure to be smooth. Under some assumptions on the representation of the dual space of such a ...
[EN] Following Schachermayer, a subset B of an algebra A of subsets of Ω is said to have the N-property if a B-pointwise bounded subset Mof ba(A)is uniformly bounded on A, where ba(A) is the Banach space of the real ...
[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 ...
Sánchez Pérez, Enrique Alfonso(Akademie věd České republiky, Matematický ústav, 2015)
In this paper we analyse a definition of a product of Banach spaces that
is naturally associated by duality with a space of operators that can be considered as
a generalization of the notion of space of multiplication ...
Jiménez Fernández, Eduardo; Juan Blanco, María Aranzazu; Sánchez Pérez, Enrique Alfonso(Belgian Mathematical Society, 2018)
[EN] Consider an abstract Banach lattice. Under some mild assumptions, it can be identi¿ed with a Banach ideal of integrable functions with respect to a (non necessarily ¿-¿nite) vector measure on a ¿-ring. Extending some ...
Calabuig Rodriguez, Jose Manuel; Juan Blanco, María Aránzazu; Sánchez Pérez, Enrique Alfonso(ELEMENT, 2012)
[EN] The lattice properties of the Banach lattices
Lp(m) and Lpw(m) of p-integrable real-valued functions and weakly p-integrable
real-valued functions with respect to a vector measure m defined on a delta-ring are ...
Let be a p-convex () order continuous Banach function space over a positive finite measure . We characterize the subspaces of which can be found simultaneously in and a suitable space, where is a positive finite measure ...
Calabuig, J. M.; Rodriguez, J.; Sánchez Pérez, Enrique Alfonso(John Wiley & Sons, 2017)
[EN] We show a picture of the relations among different types of summability of series in the space L-1(m) of integrable functions with respect to a vector measure m of relatively norm compact range. In order to do that, ...
Calabuig, J. M.; Jiménez Fernández, Eduardo; Juan Blanco, María Aránzazu; Sánchez Pérez, Enrique Alfonso(Springer Verlag, 2016-03)
We provide a tensor product representation of Kothe-Bochner function spaces of vector valued integrable functions. As an application, we show that the dual space of a Kothe-Bochner function space can be understood as a ...