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 10

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 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.
Compact operators and approximation spaces
(Colloquium mathematicum, 2014) Cobos Díaz, Fernando; Domínguez Bonilla, Óscar; Martínez, Antón
We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.
Inclusion indices of Quasi-Banach Spaces
(Bollettino della Unione Matematica Italiana. Sezione B: articoli di Bollettino dell unione matematica italiana. Sezione B: articoli di ricerca matematica, 2007) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano Rodríguez, Antonio; Martínez, Antón
Abstract K and J Spaces and Measure of Non-Compactness
(Mathematische Nachrichten, 2007) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice Γ. The formula is given in terms of the norms of the shift operators in Γ.
Interpolation of compact bilinear operators among quasi-Banach spaces and applications
(Mathematische Nachrichten, 2018) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We study the interpolation properties of compact bilinear operators by the general real method among quasi- Banach couples. As an application we show that commutators of Calderón-Zygmund bilinear operators S : Lp × Lq -? Lr are compact provided that 1/2 < r < 1, 1 < p, q < 8 and 1/p + 1/q = 1/r.