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 26

Measure of non-compactness and limiting interpolation with slowly varying functions
(Banach Journal of Mathematical Analysis, 2024) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Grover, Manvi
We give estimates for the measure of non-compactness of an operator interpolated by the limiting methods involving slowly varying functions. As applications we establish estimates for the measure of non-compactness of operators acting between Lorentz–Karamata spaces.
On compactness results of Lions-Peetre type for bilinear operators
(Nonlinear Analysis, 2019) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
Let Ā = (A₀ , A₁) , B̄ = (B₀ , B₁) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ||T(a, b)||ᴇ ≤ M[sub]j ||a||ᴀ[sub]j ||b||ʙ[sub]j for a ∈ A₀ ∩ A₁, b ∈ B₀ ∩ B₁, j = 0, 1. If T : A°[sub]j × B°[sub]j −→ E compactly for j = 0 or 1, we show that T may be uniquely extended to a compact bilinear operator from the complex interpolation spaces generated by Ā and B̄ to E. Furthermore, the corresponding result for the real method is given and we also study the case when E is replaced by a couple (E₀, E₁) of Banach function spaces on the same measure space.
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.
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 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 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.
Real Interpolation and Closed Operator Ideals
(Journal de Mathématiques Pures et Appliquées, 2004) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martínez, Antón
We investigate the behaviour by general J- and K-methods of certain closed operator ideals. In particular, the results apply to weakly compact operators, Rosenthal operators and Banach–Saks operators.
Remarks on Compact Operators between Interpolation Spaces associated to Polygons
(Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas, 2006) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
This note deals with interpolation methods dened by means of polygons. We show necessary and sufcient conditions for compactness of operators acting from a J-space into a K-space.