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 28

On a result of Peetre about interpolation of operator spaces
(Publicacions Matemàtiques, 2000) Cobos Díaz, Fernando; Signes, Teresa
We establish interpolation formulae for operator spaces that are components of a given quasi-normed operator ideal.
Quaternary binary trilinear forms of norm unity
(Proceedings of the Estonian Academy of Sciences, 2006) Bernhardsson, Bo; Cobos Díaz, Fernando; Kühn, Tomas; Mondoc, Daniel; Peetre, Jaak
So far trilinear forms have mostly been considered in low dimensions, in particular the dimension two (binary) case, and when the ring of scalars K is either the real numbers R or the complex ones C. The main aim in both situations has been to decide when a normalized form has norm unity. Here we consider the case of quaternions, K = H. This note is rather preliminary, and somewhat experimental, where the computer program Mathematica plays a certain role. A preliminary result obtained is that the form has norm unity if and only if the discriminant of a certain 5-dimensional quadratic form has all its principal minors nonnegative. We found also a rather unexpected similarity between the noncommutative case of Hnand the commutative one of R and C.
Logarithmic Interpolation Spaces Between Quasi-Banach Spaces
(Zeitschrift Fur Analysis Und Ihre Anwendungen, 2007) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martinez, Antón
Let A0 and A1 be quasi-Banach spaces with A0 ,! A1. By means of a direct approach, we show that the interpolation spaces on (A0;A1) generated by the function parameter tµ(1 + j log tj)¡b can be expressed in terms of classical real inter-polation spaces. Applications are given to Zygmund spaces Lp(log L)b(), Lorentz-Zygmund function spaces and operator spaces de¯ned by using approximation num- bers.
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 Function Spaces by Methods Defined by Means of Polygons
(Journal of Approximation Theory, 2005) Cobos Díaz, Fernando; Martín, Joaquim
We describe the spaces obtained by applying the interpolation methods associated to polygons to N-tuples of weighted Lp-spaces, N-tuples of classical Lorentz spaces and some other N-tuples of function spaces.
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.
On Strictly Singular and Strictly Cosingular Embeddings Between Banach Lattices of Functions
(Mathematical Proceedings of the Cambridge Philosophical Society, 2002) Cobos Díaz, Fernando; Pustylnik, E.
Let E be a Banach function lattice such that L1[0; 1] ,! E ,! L1[0; 1]. We characterize the strict singularity of the embedding L1[0; 1] ,! E and the strict cosingularity of E ,! L1[0; 1] in terms of functionals de_ned by using characteristic functions.
Real Interpolation and Closed Operator Ideals
(Journal de Mathématiques Pures et Appliquées, 2004) Cobos Díaz, Fernando; Fernández-Cabrera Marín, Luz María; Manzano, Antonio; Martínez, Antón
We investigate the behaviour by general J- and K-methods of certain closed operator ideals. In particular, the results apply to weakly compact operators, Rosenthal operators and Banach–Saks operators.