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
56 results
Search Results
Now showing 1 - 10 of 56
Item Norm Estimates for Interpolation Methods Defined by Means of Polygons(Journal of Approximation Theory, 1995) Cobos Díaz, Fernando; Fernández Martínez, Pedro; Schonbek, TomasWe study interpolation methods associated to polygons and establish estimates for the norms of interpolated operators. Our results explain the geometrical base of estimates in the literature. Applications to interpolation of weighted L(p)-spaces are also given.Item On duality between K- and J-spaces(Proceedings of the Edinburgh Mathematical Society, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón; Raynaud, YvesWe 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 latticesItem On a result of Peetre about interpolation of operator spaces(Publicacions Matemàtiques, 2000) Cobos Díaz, Fernando; Signes, TeresaWe establish interpolation formulae for operator spaces that are components of a given quasi-normed operator ideal.Item On a Theorem by Lions and Peetre about Interpolation between a Banach Space and its Dual(Houston Journal of Mathematics, 1998) Cobos Díaz, Fernando; Schonbek, TomasWe show that if the duality between a Banach space A and its anti-dual A* is given by the inner product of a Hilbert space H, then (A, A*)1/2,2 = H = (A,A*)[l,2~, provided A satisfies certain mild conditions. We do not assume A is reflexive. Applications are given to normed ideals of operators.Item On G(p)-classes of trilinear forms(Journal of the London Mathematical Society. Second Series, 1999) Cobos Díaz, Fernando; Kuehn, Thomas; Peetre, JaakIn a previous paper, the authors laid the foundations of a theory of Schatten±von Neumann classes 'p (0!p%¢) of trilinear forms in Hilbert space. This paper continues that research. In the n-dimensional case, it is shown that the best constant d# that relates the Hilbert±Schmidt norm of a form with its bounded norm behaves like n. Some results are also obtained in the quasi-Banach case (0!p!1), and for twobounded forms. Finally, the domination problem is investigated in the trilinear set-up.Item On Hardy's inequality and eigenvalue distributions(Portugaliae mathematica, 1993) Cobos Díaz, Fernando; Resina, IvamWe show a direct proof for the generalized Hardy’s inequality obtained by the first author Math. Nachr. 126, 281-300, 1986. Our techniques are elementary and work in the limit case which was not covered in [loc. cit.]. Some applications to eigenvalue distributions of operator ideals are also given.Item Quantitative Estimates for Interpolated Operators by Multidimensional Methods(Revista matemática complutense, 1999) Cobos Díaz, Fernando; Cordeiro, José María; Martínez, AntónWe describe the behavior of ideal variations under interpolation methods associated to polygons.Item 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, JaakSo 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.Item 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, AntónLet 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.Item Measure of non-compactness and interpolation methods associated to polygons(Glasgow Mathematical Journal, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, AntónWe 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.