Person: Cobos Díaz, Fernando
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First Name
Fernando
Last Name
Cobos Díaz
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Ciencias Matemáticas
Department
Análisis Matemático Matemática Aplicada
Area
Análisis Matemático
Identifiers
45 results
Search Results
Now showing 1 - 10 of 45
Item 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, ManviWe 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.Item Diversity of Lorentz-Zygmund spaces of operators defined by approximation numbers(Analysis Mathematica, 2023) Cobos Díaz, Fernando; Kühn, ThomasWe prove the following dichotomy for the spaces ℒ (a) p,q,α (X, Y) of all operators T ∈ ℒ(X, Y) whose approximation numbers belong to the Lorentz-Zygmund sequence spaces ℓp,q(log ℓ)α: If X and Y are infinite-dimensional Banach spaces, then the spaces ℒ (a) p,q,α (X, Y) with 0 < p < ∞, 0 < q ≤ ∞ and α ∈ ℝ are all different from each other, but otherwise, if X or Y are finite-dimensional, they are all equal (to ℒ(X, Y)). Moreover we show that the scale is strictly increasing in q, where ℒ (a) ∈,q (X, Y) is the space of all operators in ℒ(X, Y) whose approximation numbers are in the limiting Lorentz sequence space ∓∈,q.Item Logarithmic interpolation methods and measure of non-compactness(Quarterly Journal of Mathematics, 2019) Cobos Díaz, Fernando; Fernández Besoy, BlancaWe derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with θ = 0, 1 between quasi-Banach spaces. Applications are given to operators between Lorentz-Zygmund spaces.Item Approximation and entropy numbers of embeddings between approximation spaces(Constructive Approximation, 2018) Cobos Díaz, Fernando; Domínguez Bonilla, Óscar; Kühn, ThomasItem 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, AntónLet 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.Item Measure of non-compactness and interpolation methods associated to polygons(Glasgow Mathematical Journal, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, AntónWe 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.Item Lorentz-Schatten classes and pointwise domination of matrices(Canadian Mathematical Bulletin, 1999) Cobos Díaz, Fernando; Kühn, ThomasWe investigate pointwise domination property in operator spaces generated by Lorentz sequence spacesItem 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, AntónWe 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.Item On interpolation of Asplund operators(Mathematische Zeitschrift, 2005) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martínez, AntónWe study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.Item On Interpolation of Compact Nonlinear Operators(Bulletin of the London Mathematical Society, 1990) Cobos Díaz, FernandoWe 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.