Person: Fernández-Cabrera Marín, Luz María
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First Name
Luz María
Last Name
Fernández-Cabrera Marín
Affiliation
Universidad Complutense de Madrid
Faculty / Institute
Estudios estadísticos
Department
Análisis Matemático Matemática Aplicada
Area
Matemática Aplicada
Identifiers
17 results
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Now showing 1 - 10 of 17
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 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 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 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.Item On the Relationship between Interpolation of Banach Algebras and Interpolation of Bilinear Operators(Canadian Mathematical Bulletin, 2010) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz MaríaWe show that if the general real method (. , .)(Gamma) preserves the Banach-algebra Structure, then a bilinear interpolation theorem holds for (. , .)(Gamma).Item On interpolation of weakly compact bilinear operators(Mathematische Nachrichten, 2022) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, AntónWe 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.Item 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, AntónWe 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.Item Remarks on Entropy Numbers, Measure of Non-compactness and Interpolation(Advances in Mathematics, 2012) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz MaríaWe review the interpolation properties of entropy numbers and the measure of non-compactness. We describe the classical results as well as several very recent results.Item Weakly compact bilinear operators among real interpolation spaces(Journal of Mathematical Analysis and Applications, 2022) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz MaríaWe show a necessary and sufficient condition for weak compactness of bilinear operators interpolated by the real method. This characterization does not hold for interpolated operators by the complex method.Item Duality for logarithmic interpolation spaces and applications to Besov spaces(Banach center publications, 2020) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz MaríaWe review several results on duality of logarithmic interpolation spaces and applications to Besov spaces. We also establish some new results on Besov spaces with smoothness close to zero defined by differences.