Información del autor
Autor Cobos, Fernando |
Documentos disponibles escritos por este autor (121)
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We establish two-sided estimates for entropy numbers of embeddings between certain weighted Banach sequence spaces with mixed norms. These estimates are‘‘almost’’ sharp, in the sense that upper and lower bounds differ only by logarithmic terms a[...]![]()
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We consider limiting real interpolation spaces defined by using powers of iterated logarithms and show their description by means of the J -functional. Our results allow to complement some estimates on approximation of stochastic integrals.![]()
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We study spectral properties of operators on logarithmic perturbations of the real interpolation spaces with ? = 0 or 1. We also establish estimates for the measure of non-compactness of operators interpolated by those methods.![]()
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We provide a simple algorithm that constructs an exact minimizer for the E-functional E(t, f ; L?, BV) = inf ?g?L??t ? f ? g?BV . Here L?, BV stand for the space of bounded functions and the space of functions with bounded variation on the inter[...]![]()
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We establish abstract extrapolation results for entropy numbers of operators in Banach spaces. The results apply to extrapolation in the source spaces and also in the target spaces. As an illustration of the abstract results, applications to lim[...]![]()
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We establish compactness results for extrapolation constructions which correspond to the well-known Lions-Peetre compactness theorems of interpolation theory. Applications are given to compactness of certain limiting Sobolev embeddings.![]()
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The paper establishes estimates for ideal measures of operators interpolated by the real method in terms of the measures of their restrictions to a sequence of spaces modelled on the intersection. It also shows that the estimates are optimal.![]()
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We 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-[...]![]()
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Cobos, Fernando ; Fernández-Cabrera, Luz M. | Institute of Mathematics. Polish Academy of Sciences | 2008We review several results on interpolation of Banach algebras and factorization of weakly compact homomorphisms. We also establish a new result on interpolation of multilinear operators.![]()
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The paper deals with the entropy ideals generated by the Lorentz- Marcinkiewicz spaces of the type ? ? (?) where ? is a function parameter. The entropy ideal generated by ? ? (?) is the set of all operators between Banach spaces whose sequence o[...]![]()
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Fernández-Cabrera, Luz M. ; Cobos, Fernando ; Hernández, Francisco L. ; Sánchez, Víctor M. | Cambridge University Press | 2004We study inclusion indices relative to an interpolation scale. Applications are given to several families of functions spaces.![]()
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Let (Y0, Y1) be a Banach couple and let Xj be a closed complemented subspace of Yj ; (j = 0; 1). We present several results for the general problem of finding necessary and sufficient conditions on the parameters (?, q) such that the real interp[...]![]()
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We study the interpolation properties of compact bilinear operators by the general real method among quasi- Banach couples. As an application we show that commutators of Calderón-Zygmund bilinear operators S : Lp × Lq -? Lr are compact provided [...]![]()
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We show that the classical Lions-Peetre compactness theorems for Banach spaces (which are the main tools for proving all known compactness results in interpolation theory) fail in the locally convex case. We also prove a positive result assuming[...]![]()
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We 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 op[...]![]()
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Cobos, Fernando ; Fernández-Martínez, Pedro ; Martínez, Antón | Polish Acad Sciencies Inst Mathematics | 1999We 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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Working in the setting of quasi-Banach couples, we establish a formula for the measure of non-compactness of bilinear operators interpolated by the general real method. The result applies to the real method and to the real method with a function[...]![]()
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We develop a method suitable for interpolation of uniformly absolutely continuous operators. We then apply this method to establishing compactness of operators and embeddings especially in the limiting situations, where the classical interpolati[...]![]()
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Given an operator ideal J , the author describes the behaviour under interpolation of deviations of a linear operator T from the closed surjective hull of J and the closed injective hull of J . General results obtained in a collaboration with A.[...]![]()
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We investigate limiting J-interpolation methods for general Banach couples, not necessarily ordered. We also show their relationship with the interpolation methods defined by the unit square.![]()
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We study limiting K- and J-methods for arbitrary Banach couples. They are related by duality and they extend the methods already known in the ordered case. We investigate the behaviour of compact operators and we also discuss the representation [...]![]()
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Working with interpolation methods associated to polygons, a result of Cobos and Peetre guarantees that the interpolated operator is compact provided all but two restrictions of the operator (located in adjacent vertices) are compact. We charact[...]