Información del autor
Autor Hernández, Francisco L. |
Documentos disponibles escritos por este autor (21)
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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[...]![]()
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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[...]![]()
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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 [...]![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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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 -->[...]![]()
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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.![]()
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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[...]![]()
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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[...]![]()
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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[...]![]()
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Hernández, Francisco L. ; Sánchez de los Reyes, Víctor Manuel ; Semenov, Evgeny M. | Elsevier | 2004-03-15Strict singularity and strict co-singularity of inclusions between symmetric sequence spaces are studied. Suitable conditions are provided involving the associated fundamental functions. The special case of Lorentz and Marcinkiewicz spaces is ch[...]![]()
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An operator A mapping a Banach space E into a Banach space F is called strictly singular (or Kato) if any restriction of A to an infinite-dimensional subspace of E is not an isomorphism. The paper deals with the problem of describing all co[...]![]()
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Sánchez de los Reyes, Víctor Manuel ; Semenov, Evgeny M. ; Hernández, Francisco L. | Interperiodica | 2005The paper deals with the strict singularity and the disjoint strict singularity of the canonical embedding between couples of rearrangement invariant spaces E and F. Let E c F. This embedding is called strictly singular (disjointly strictly sing[...]![]()
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Hernández, Francisco L. ; Sánchez de los Reyes, Víctor Manuel ; Semenov, Evgeny M. | Springer | 2008-01It is given a complete characterization of the strict singularity and the disjoint strict singularity of the inclusions E ? L1 + L? for the class of rearrangement invariant function spaces E on the [0,?) interval. Their relationship is also anal[...]![]()
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Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L[...]![]()
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Hernández, Francisco L. ; Semenov, Evgeny M. ; Tradacete Pérez, Pedro | American Mathematical Society | 2010-02We study the class Vp of strictly singular non-compact operators on Lp spaces. This allows us to obtain interpolation results for strictly singular operators on Lp spaces. Given 1 ? p