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

Full item page

Search Results

Now showing 1 - 10 of 15

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.
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 Asplund operators
(Mathematische Zeitschrift, 2005) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martínez, Antón
We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.
On interpolation of the measure of noncompactness
(Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 2006) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.
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 interpolation of strictly singular operators, strictly co-singular operators and related operator ideals
(Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000) Cobos Díaz, Fernando; Manzano, A.; Martínez, Antón; Matos, P.
We improve the known results on interpolation of strictly singular operators and strictly co-singular operators in several directions. Applications are given to embeddings between symmetric spaces.
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 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 interpolation of the measure of non-compactness of bilinear operators with weak assumptions on the boundedness of the operator
(Journal of Mathematical Analysis and Applications, 2021) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We complete the range of the parameters in the interpolation formula established by Mastyło and Silva for the measure of non-compactness of a bilinear operator interpolated by the real method.
Compactness interpolation results for bilinear operators of convolution type and for operators of product type
(Journal of Approximation Theory, 2022) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We establish compactness interpolation results for bilinear operators of convolution type and for operators of product type among quasi-Banach spaces. We do not assume any auxiliary condition on the spaces.