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Given a measurable space (Omega, mu) and a sequence of disjoint measurable subsets A = (A(n))(n), the associated averaging projection P-A and the orthogonal projection T-A are considered. We study the boundedness of these operators on variable e[...]texto impreso
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Hernández, Francisco L. ; Sánchez de los Reyes, Víctor Manuel ; Semenov, Evgeny M. | Polish Acad Sciencies Inst Mathematics | 2001It is studied when inclusions between rearrangement invariant function spaces on the interval [0, infinity) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions L 1[...]texto impreso
This is a survey on disjointly homogeneous Banach lattices and their applications. Several structural properties of this class are analyzed. In addition we show how these spaces provide a natural framework for studying the compactness of powers [...]texto impreso
We study several properties of disjointly homogeneous Banach lattices with a special focus on two questions: the self-duality of this class and the existence of disjoint sequences spanning complemented subspaces. Various results around these pro[...]texto impreso
García del Amo Jiménez, Alejandro José ; Hernández, Francisco L. ; Sánchez de los Reyes, Víctor Manuel ; Semenov, Evgeny M. | London Mathematical Society | 2000A linear operator between two Banach spaces X and Y is strictly-singular (or Kato) if it fails to be an isomorphism on any infinite dimensional subspace. A weaker notion for Banach lattices introduced in [8] is the following one: an operator T f[...]texto impreso
García del Amo Jiménez, Alejandro José ; Hernández, Francisco L. ; Ruiz Bermejo, César | Cambridge University Press | 1996Interpolation properties of the class of disjointly strictly singular operators on Banach lattices are studied. We also give some applications to compare the lattice structure of two rearrangement invariant function spaces. In particular, we obt[...]texto impreso
We prove that each positive operator from a Banach lattice E to a Banach lattice F with a disjointly strictly singular majorant is itself disjointly strictly singular provided the norm on F is order continuous. We prove as well that if S : E -->[...]texto impreso
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Fernández-Cabrera, Luz M. ; Cobos, Fernando ; Hernández, Francisco L. ; Sánchez, Víctor M. | Cambridge University Press | 2004We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.texto impreso
We study the interpolation and extrapolation properties of strictly singular operators between different Lp spaces. To this end, the structure of strictly singular non-compact operators between L-p Lq spaces is analyzed. Among other things, we c[...]texto impreso
It is shown that a separable variable exponent (or Nakano) function space L-p(.)(?) has a lattice-isomorphic copy of l(q) if and only if q is an element of Rp(.), the essential range set of the exponent function p(.). Consequently Rp(.) is a lat[...]texto impreso
Hernández, Francisco L. ; Ruiz Bermejo, César ; Sánchez de los Reyes, Víctor Manuel | Elsevier | 2015-11Let I1 and I2 be arbitrary operator ideals in the sense of Pietsch and E and F be Banach spaces such that the set I1(E,F){set minus}I2(E,F) is non-empty. We give a quite general sufficient condition on the Banach spaces in order to obtain the sp[...]texto impreso
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