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 27

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, Antón
We show abstract versions for Banach couples of several limiting compact interpolation theorems established by Edmunds and Opic for couples of Lp spaces.
On compactness results of Lions-Peetre type for bilinear operators
(Nonlinear Analysis, 2019) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
Let 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.
On duality between K- and J-spaces
(Proceedings of the Edinburgh Mathematical Society, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón; Raynaud, Yves
We study the relationship between the dual of the #C-space defined by means of a polygon and the /-space generated by the dual N-tuple. The results complete the research started in [4]. Special attention is paid to the case when the N-tuple is formed by Banach lattices
Quantitative Estimates for Interpolated Operators by Multidimensional Methods
(Revista matemática complutense, 1999) Cobos Díaz, Fernando; Cordeiro, José María; Martínez, Antón
We describe the behavior of ideal variations under interpolation methods associated to polygons.
Measure of non-compactness and interpolation methods associated to polygons
(Glasgow Mathematical Journal, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón
We 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.
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, Antón
We 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.
On interpolation of Asplund operators
(Mathematische Zeitschrift, 2005) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martínez, Antón
We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.
On interpolation of the measure of noncompactness
(Proceedings of the Estonian Academy of Sciences. Physics. Mathematics, 2006) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Martínez, Antón
We revised the known results on interpolation of the measure of noncompactness and we announce a new approach to establishing the interpolation formula for the real method.
On interpolation of bilinear operators by methods associated to polygons
(Bollettino della Unione Matematica Italiana, 1999) Cobos Díaz, Fernando; Cordeiro, José María; Martínez, Antón
The authors investigate the behaviour of bilinear operators under interpolation by the methods associated to polygons. These methods, working with N-tuples (N _ 3) of Banach spaces instead of couples, were introduced by F. Cobos and J. Peetre [Proc. Lond. Math. Soc., III. Ser. 63, 371-400 (1991; Zbl 0727.46053)]. The main properties of methods defined by polygons are summarized and then a bilinear interpolation theorem for a combination of the K- and J-methods is established. Another bilinear interpolation theorem for the J-method is given and a counterexample shows that a similar result fails for the K-method. The final part contains an application to interpolation of operator spaces starting from Banach lattices.
On interpolation of strictly singular operators, strictly co-singular operators and related operator ideals
(Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000) Cobos Díaz, Fernando; Manzano, A.; Martínez, Antón; Matos, P.
We improve the known results on interpolation of strictly singular operators and strictly co-singular operators in several directions. Applications are given to embeddings between symmetric spaces.