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
54 results
Search Results
Now showing 1 - 10 of 54
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 Abstract limit J-spaces(Journal of the London Mathematical Society, 2010) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Mastylo, MieczyslawWe investigate the limit J-spaces corresponding to the general real method. These interpolation spaces are defined by Banach sequence lattices and include those spaces that arise by the choice θ = 0 in the definition of the real method. We pay especial attention to spaces generated by rearrangement-invariant sequence spaces. We establish necessary and sufficient conditions for compactness of interpolated operators between limit J-spaces. We also study the relationships between J- and K-spaces and we derive some interpolation formulae for notable couples of function spaces, couples of spaces of operators and also couples of sequence spaces.Item Approximation spaces, limiting interpolation and Besov spaces(Journal of Approximation Theory, 2015) Cobos Díaz, Fernando; Domínguez, OscarWith the help of limiting interpolation we determine the spaces obtained by iteration of approximation constructions. Then we apply the reiteration formula and limiting interpolation to investigate several problems on Besov spaces, including embeddings in Lorentz-Zygmund spaces and distribution of Fourier coefficients.Item An interpolation formula for approximation spaces(Interpolation spaces and related topics, 1992) Cobos Díaz, Fernando; Resina, Ivam; Cwikel, M.; Milman, Mario; Rocherg, RichardItem 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, AntónWe 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.Item Compact operators between K - and J -spaces(Studia Mathematica, 2005) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, AntónThe paper establishes necessary and sufficient conditions for compactness of operators acting between general K -spaces, general J -spaces and operators acting from a J -space into a K -space. Applications to interpolation of compact operators are also given.Item Compact embeddings of Brezis-Wainger type(Revista Matemática Iberoamericana, 2006) Cobos Díaz, Fernando; Kühn, Thomas; Schonbek, TomasLet Ω be a bounded domain in Rn and denote by idΩ the restriction operator from the Besov space B1+n/p pq (Rn) into the generalized Lipschitz space Lip(1,−α)(Ω). We study the sequence of entropy numbers of this operator and prove that, up to logarithmic factors, it behaves asymptotically like ek(idΩ) ∼ k−1/p if α > max (1 + 2/p −1/q, 1/p). Our estimates improve previous results by Edmunds and Haroske.