Person:
Cobos Díaz, Fernando

First Name

Fernando

Last Name

Cobos Díaz

URI

https://hdl.handle.net/20.500.14352/75635

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Análisis Matemático Matemática Aplicada

Area

Análisis Matemático

Identifiers

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Now showing 1 - 10 of 21

Logarithmic Interpolation Spaces Between Quasi-Banach Spaces
(Zeitschrift Fur Analysis Und Ihre Anwendungen, 2007) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martinez, Antón
Let A0 and A1 be quasi-Banach spaces with A0 ,! A1. By means of a direct approach, we show that the interpolation spaces on (A0;A1) generated by the function parameter tµ(1 + j log tj)¡b can be expressed in terms of classical real inter-polation spaces. Applications are given to Zygmund spaces Lp(log L)b(), Lorentz-Zygmund function spaces and operator spaces de¯ned by using approximation num- bers.
Measure of non-compactness and interpolation methods associated to polygons
(Glasgow Mathematical Journal, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón
We establish an estimate for the measure of non-compactness of an interpolated operator acting from a J-space into a K-space. Our result refers to general Banach N-tuples. We also derive estimates for entropy numbers if some of the N-tuples reduce to a single Banach space.
Lorentz-Schatten classes and pointwise domination of matrices
(Canadian Mathematical Bulletin, 1999) Cobos Díaz, Fernando; Kühn, Thomas
We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces
On interpolation of Banach algebras and factorization of weakly compact homomorphisms
(Bulletin des Sciences Mathematiques, 2006) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We show a necessary and sufficient condition on the lattice Γ for the general real method (· , ·)Γ to preserve the Banach-algebra structure. As an application we derive factorization of weakly compact homomorphisms through interpolation properties of weakly compact operators.
On Interpolation of Compact Nonlinear Operators
(Bulletin of the London Mathematical Society, 1990) Cobos Díaz, Fernando
We prove that the classical Lions-Peetre compactness theorems for linear operators still hold for Lipschitz operators. As a consequence, we deduce that certain Uryson integral operators are compact. We also show that Lipschitz operators can be interpolated by a wide class of J-functors.
On interpolation of weakly compact bilinear operators
(Mathematische Nachrichten, 2022) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We study the interpolation properties of weakly compact bilinear operators by the real method and also by the complex method. We also study the factorization property of weakly compact bilinear operators through reflexive Banach spaces.
On nuclearity of embeddings between Besov spaces
(Journal of Approximation Theory, 2018) Cobos Díaz, Fernando; Domínguez Bonilla, Óscar; Kühn, Thomas
Let Bp,qs,α(Ω) be the Besov space with classical smoothness s and additional logarithmic smoothness of order α on a bounded Lipschitz domain Ω in Rd. For s1, s2 ∈ R, 1 ≤ p1, p2, q1, q2 ≤ ∞ and s1 − s2 = d − d(1/p2 − 1/p1)+, we show a suﬃcient condition on q1, q2 for nuclearity of embedding Bs1,α1 (superíndices) y p1, q1 (subíndices)(Ω) → Bp2,α2 (superíndice) y s2 q,2 (subíndices) (Ω). We also show that the condition is necessary in a wide range of parameters.
On reiteration and the behaviour of weak compactness under certain interpolation methods
(Collectanea mathematica, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón
This article deals with K- and J-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compactness results.
On the connection between real and complex interpolation of quasi-Banach spaces
(Bulletin des sciences Mathematiques, 1998) Cobos Díaz, Fernando; Peetre, Jaak; Persson, Lars Erick
We describe a new approach to interpolate by the complex method quasi-Banach couples formed by real-intermediate spaces. End-point cases are also considered, and applications are given to function spaces and to operator spaces.
On Strictly Singular and Strictly Cosingular Embeddings Between Banach Lattices of Functions
(Mathematical Proceedings of the Cambridge Philosophical Society, 2002) Cobos Díaz, Fernando; Pustylnik, E.
Let E be a Banach function lattice such that L1[0; 1] ,! E ,! L1[0; 1]. We characterize the strict singularity of the embedding L1[0; 1] ,! E and the strict cosingularity of E ,! L1[0; 1] in terms of functionals de_ned by using characteristic functions.