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
132 results
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Now showing 1 - 10 of 132
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 On a paper of Edmunds and Opic on limiting interpolation of compact operators between L-p spaces(Mathematische Nachrichten, 2015) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, AntónWe show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.Item Norm Estimates for Interpolation Methods Defined by Means of Polygons(Journal of Approximation Theory, 1995) Cobos Díaz, Fernando; Fernández Martínez, Pedro; Schonbek, TomasWe study interpolation methods associated to polygons and establish estimates for the norms of interpolated operators. Our results explain the geometrical base of estimates in the literature. Applications to interpolation of weighted L(p)-spaces are also given.Item Nuclear embeddings of Besov spaces into Zygmund spaces(Journal of Fourier analysis and applications, 2019) Cobos Díaz, Fernando; Edmunds, David E.; Kühn, TomasLet d ∈ N and let Ω be a bounded Lipschitz domain in Rd. We prove that the embedding Id : Bd (Ω) −→ L (log L) (Ω) is nuclear if a < −1 and 1 ≤ p, q ≤ ∞,p,q ≤∞, while if −1 < a < 0, 2 < p < ∞ and p ≤ q ≤ ∞ while if −1 < a < 0, 2 < p < ∞ and p ≤ q ≤ ∞ the embedding Id fails to be nuclear. Furthermore, if a = −1, the embedding Id : Bd∞,∞(Ω) −→ L∞ (log L)−1 (Ω) is not nuclear.Item On a paper of Edmunds and Opic on limiting interpolation of compact operators between Lp spaces(Mathematische Nachrichten, 2015) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, A.We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.Item On a Conjecture of Barry Simon on Trace Ideals(Duke mathematical journal, 1989) Cobos Díaz, Fernando; Kühn, ThomasLet H denote a Hilbert space, T a compact operator on H, {sn(T)}1 n=1 the eigenvalues of |T|, and Sp (p > 0) the set of all such T for which {sn(T)}1 n=1 is in `p. If A and B are bounded linear operators on L2, say that B pointwise dominates A if |A(x)(t)| B(|x|)(t) a.e. for all x(t) in L2. It is known that if p = 2n for some positive integer n, B is in Sp, and B pointwise dominates A, then A is also in Sp. Simon has conjectured that this result fails for p < 2, and has given a counterexample for 0 < p 1. The authors provide a counterexample for the remaining cases where 1 < p < 2.Item On compactness results of Lions-Peetre type for bilinear operators(Nonlinear Analysis, 2019) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, AntónLet 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.