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
10 results
Search Results
Now showing 1 - 10 of 10
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 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 On the connection between real and complex interpolation of quasi-Banach spaces(Bulletin des sciences Mathematiques, 1998) Cobos Díaz, Fernando; Peetre, Jaak; Persson, Lars ErickWe describe a new approach to interpolate by the complex method quasi-Banach couples formed by real-intermediate spaces. End-point cases are also considered, and applications are given to function spaces and to operator spaces.Item Remarks on symmetries of trilinear forms(Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales., 2000) Cobos Díaz, Fernando; Kühn, Thomas; Peetre, JaakWe investigate the interplay between the different kinds of symmetry that a trihnear form may have and the behaviour of its norm.Item Schatten-Vonneumann Classes of Multilinear Forms(Duke mathematical journal, 1992) Cobos Díaz, Fernando; Kühn, Thomas; Peetre, JaakThe authors establish a number of results concerning normed ideals of multilinear forms in Banach spaces which extend the theory of trace ideals of operators on Hilbert space to such multilinear forms. For example, it is shown that the dual of the space of compact forms is the space of nuclear forms, while the second dual is the space of bounded forms. Moreover, a direct analogue of the Schatten p-ideals of operators on Hilbert space is defined using interpolation techniques and a normal form for compact forms is introduced.Item Interpolation of Compactness using Aronszajn-Gagliardo Functors(Israel Journal of Mathematics, 1989) Cobos Díaz, Fernando; Peetre, JaakItem Extreme points of the complex binary trilinear ball(Studia Mathematica, 2000) Cobos Díaz, Fernando; Kühn, Thomas; Peetre, JaakWe characterize all the extreme points of the unit ball in the space of trilinear forms on the Hilbert space C-2. This answers a question posed by R. Grzaslewicz and K. John [7], who solved the corresponding problem for the real Hilbert space R-2. As an application we determine the best constant in the inequality between the Hilbert-Schmidt norm and the norm of trilinear forms.Item Multilinear forms of Hilbert type and some other distinguished forms(Integral Equations and Operator Theory, 2006) Cobos Díaz, Fernando; Kühn, Thomas; Peetre, JaakWe give some new examples of bounded multilinear forms on th Hilbert spaces 2 and L2(0,∞). We characterize those which are compact or Hilbert-Schmidt. In particular, we study m-linear forms (m ≥ 3) on 2 which can be regarded as the multilinear analogue of the famous Hilbert matrix. We also determine the norm of the permanent on Kn, where K = R or C.Item A Multidimensional Wolff Theorem(Studia Mathematica, 1989) Cobos Díaz, Fernando; Peetre, JaakThe authors consider multiparameter scales of interpolation spaces and prove a general form of the Wolff reiteration theorem [cf. T. H. Wolff, Lecture Notes Math. 908, 199- 204 (1982)] for n- tuples of Banach spaces. The proof, based on the use of the Aronszajn- Gagliardo orbit and co-orbit functors, is an adaptation of previous work by S. Janson, P. Nilsson, J. Peetre and M. Zafran [Proc. London Math. Soc., III.Ser. 48, 283-299 (1984)].Item Interpolation of Compact-Operators: The Multidimensional Case(Proceedings of the London Mathematical Society, 1991) Cobos Díaz, Fernando; Peetre, JaakWe investigate how compact operators behave under J and K interpolation methods for N spaces and two parameters. First we study those methods: relationship with those already existing in the literature, estimates for the norms of interpolated operators, examples, characterization as Aronszajn-Gagliardo functors,.... We also describe the relationship between Sparr and Fernandez methods and we derive sharp estimates for the norms of interpolated operators in Fernandez' case. Then we investigate the behaviour of compact operators. We begin with the case when one of the N-tuples reduces to a single Banach space, and later we treat the general case by means of the approach developed in [8].