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 18

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.
Abstract limit J-spaces
(Journal of the London Mathematical Society, 2010) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Mastylo, Mieczyslaw
We 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.
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, Antón
We 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.
Compact operators between K - and J -spaces
(Studia Mathematica, 2005) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
The 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.
Complex Interpolation, Minimal Methods and Compact Operators
(Mathematische Nachrichten, 2004) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We characterize compact operators between complex interpolation spaces and between spaces obtained by using certain minimal methods in the sense of Aronszajn and Gagliardo. Applications to interpolation of compact operators are also given.
Indices defined by Interpolation Scales and Applications
(Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004) Fernández-Cabrera Marín, Luz María; Cobos Díaz, Fernando; Hernández, Francisco L.; Sánchez, Víctor M.
We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.
Inclusion indices of Quasi-Banach Spaces
(Bollettino della Unione Matematica Italiana. Sezione B: articoli di Bollettino dell unione matematica italiana. Sezione B: articoli di ricerca matematica, 2007) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano Rodríguez, Antonio; Martínez, Antón
Abstract K and J Spaces and Measure of Non-Compactness
(Mathematische Nachrichten, 2007) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice Γ. The formula is given in terms of the norms of the shift operators in Γ.
Abstract and Concrete Logarithmic Interpolation Spaces
(Journal of the London Mathematical Society. Second Series, 2004) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Triebel, Hans
A procedure is given to reduce the interpolation spaces on an ordered pair generated by the function parameter tθ (1 + |log t|)−b to the classical real interpolation spaces. Applications are given for Lorentz–Zygmund function spaces, Besov spaces of generalized smoothness and Lorentz– Zygmund operator spaces.
Associate spaces of logarithmic interpolation spaces and generalized Lorentz-Zygmund spaces
(Annales Academiae Scientiarum Fennicae Mathematica, 2020) Besoy, Blanca F.; Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María
We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-atomic measure space, we recover results of Opic and Pick on associate spaces of generalized Lorentz-Zygmund spaces L(?,q;A). We also establish the corresponding results for sequence spaces.