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 11

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 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 bilinear operators by methods associated to polygons
(Bollettino della Unione Matematica Italiana, 1999) Cobos Díaz, Fernando; Cordeiro, José María; Martínez, Antón
The authors investigate the behaviour of bilinear operators under interpolation by the methods associated to polygons. These methods, working with N-tuples (N _ 3) of Banach spaces instead of couples, were introduced by F. Cobos and J. Peetre [Proc. Lond. Math. Soc., III. Ser. 63, 371-400 (1991; Zbl 0727.46053)]. The main properties of methods defined by polygons are summarized and then a bilinear interpolation theorem for a combination of the K- and J-methods is established. Another bilinear interpolation theorem for the J-method is given and a counterexample shows that a similar result fails for the K-method. The final part contains an application to interpolation of operator spaces starting from Banach lattices.
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 the Optimal Asymptotic Eigenvalue Behavior of Weakly Singular Integral-Operators
(Proceedings of the American Mathematical Society, 1991) Cobos Díaz, Fernando; Janson, Svante; Kühn, Thomas
We improve the known results on eigenvalue distributions of weakly singular integral operators having (power) order of the singularity equal to half of the dimension of the underlying domain. Moreover we show that our results are the best possible.
A Duality Theorem for Interpolation Methods Associated to Polygons
(Proceedings of the American Mathematical Society, 1994) Cobos Díaz, Fernando; Fernández Martínez, Pedro
We investigate dual spaces of interpolation spaces defined by means of polygons. We first show that dual spaces may fail to be intermediate spaces with respect to the dual N-tuple, and then we prove that dual spaces of J-spaces can be identified with closed subspaces of K-spaces generated by the dual N-tuple.
Interpolation of the measure of non-compactness by the real method
(Studia Mathematica, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón
We investigate the behaviour of the measure of Iron-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.
Interpolation of Compact-Operators by Goulaouic Procedure
(Studia Mathematica, 1990) Cobos Díaz, Fernando
We show that the classical Lions-Peetre compactness theorems for Banach spaces (which are the main tools for proving all known compactness results in interpolation theory) fail in the locally convex case. We also prove a positive result assuming compactness of the operator in both sides.