Person:
Cobos Díaz, Fernando

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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
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1994 - 199942000 - 20064
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Start date: 1990 × Subject: 519.6 ×

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Now showing 1 - 8 of 8
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    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.
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    A Duality Theorem for Interpolation Methods Associated to Polygons
    (Proceedings of the American Mathematical Society, 1994) Cobos Díaz, Fernando; Fernández Martínez, Pedro
    We investigate dual spaces of interpolation spaces defined by means of polygons. We first show that dual spaces may fail to be intermediate spaces with respect to the dual N-tuple, and then we prove that dual spaces of J-spaces can be identified with closed subspaces of K-spaces generated by the dual N-tuple.
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    A maximal description for the real interpolation method in the quasi-Banach case.
    (Mathematica Scandinavica, 2000) Bergh, Jöran; Cobos Díaz, Fernando
    We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces.
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    Interpolation of the measure of non-compactness by the real method
    (Studia Mathematica, 1999) Cobos Díaz, Fernando; Fernández-Martínez, Pedro; Martínez, Antón
    We investigate the behaviour of the measure of Iron-compactness of an operator under real interpolation. Our results refer to general Banach couples. An application to the essential spectral radius of interpolated operators is also given.
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    Logarithmic interpolation spaces
    (Spectral theory and nonlinear analysis with applications to spatial ecology, 2005) Cobos Díaz, Fernando; Cano-Casanova, S.; López Gómez, Julián; Mora-Corral, C.
    This volume details some of the latest advances in spectral theory and nonlinear analysis through various cutting-edge theories on algebraic multiplicities, global bifurcation theory, non-linear Schrödinger equations, non-linear boundary value problems, large solutions, metasolutions, dynamical systems, and applications to spatial ecology. The main scope of the book is bringing together a series of topics that have evolved separately during the last decades around the common denominator of spectral theory and nonlinear analysis — from the most abstract developments up to the most concrete applications to population dynamics and socio-biology — in an effort to fill the existing gaps between these fields.
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    Dependence on Parameters in Interpolation Methods Associated to Polygons
    (Bollettino della Unione Matematica Italiana, 1995) Cobos Díaz, Fernando; Fernández-Martínez, Pedro
    A theorem due to S. Janson, P. Nilsson, J. Peetre and M. Zafran [Proc. Lond. Math. Soc., III. Ser. 48, 283-299 (1984; Zbl 0532.46046)] states that for a Banach couple A such that _(A) is not closed in _(A) the real interpolation spaces A_,q and A_,p coincide if and only if _ = _ and p = q. Here the analogous problem for N-tuples of Banach spaces is investigated. It is assumed that the N-tuple A satisfies a certain condition "(A) which ensures that the J- and the K-methods with respect to a polygon _ coincide. Also, it is assumed that _(A) is not closed in _(A). The authors prove the following results: (1) If P,Q 2 int _ and AP,p = AQ,q, then p = q. (2) If P, Q,R 2 int _ and AP,q = AQ,q = AR,q, then P, Q and R are affinely dependent.
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    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.
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    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.