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We 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., DGI-CYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We establish representation theorems in terms of finite rank operators for some operator ideals defined by approximation numbers. We also study the stability under tensor product of these ideals., Spanish Ministerio de Educación y Ciencia. Programa de Cooperación con Iberoamérica, FAPESP, FAPESP-BRASIL, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We 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., Spanish Ministerio de Educación y Ciencia, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

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., Ministry of Education and Science of Spain, CAM-UCM, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We establish interpolation formulae for operator spaces that are components of a given quasi-normed operator ideal., DGES, Ministerio de Educación y Ciencia, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We show that the behaviour under interpolation of 5x-class operators is not as good as it was supposed to be. An interpolation formula for Hilbert-Schmidt operators is also established., DGICYT, US-Spain Joint Committee for Cultural and Educational Cooperation, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We 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., Spanish Ministerio de Asuntos Exteriores (Programa de Ayudas de Cooperación Científica a Investigadores en Instituciones de Suecia durante 1995)., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods., Spanish Ministerio de Ciencia y Tecnología, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We investigate pointwise domination property in operator spaces generated by Lorentz sequence spaces, DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We determine the associate space of the logarithmic interpolation space (X0, X1)1,q,A where X0 and X1 are Banach function spaces over a ?-finite measure space (?, µ). Particularizing the results for the case of the couple (L1, L?) over a non-atomic measure space, we recover results of Opic and Pick on associate spaces of generalized Lorentz-Zygmund spaces L(?,q;A). We also establish the corresponding results for sequence spaces., Ministerio de Economía y Competitividad (MINECO)/FEDER, Ministerio de Educación, Cultura y Deporte (MECD), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We prove that the classical Lions-Peetre compactness theorems for linear operators still hold for Lipschitz operators. As a consequence, we deduce that certain Uryson integral operators are compact. We also show that Lipschitz operators can be interpolated by a wide class of J-functors., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

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., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We show that certain interpolation results for compact operators established by Cobos and co-workers cannot be extended to general closed operator ideals. We shall also characterize compactness of an embedding in terms of functions related to the classical K- and J -functionals of interpolation theory., DGES, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

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., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, inpress

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., Spanish Ministerio de Ciencia y Tecnología, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

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., Spanish Ministerio de Educación y Ciencia, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We study the description by means of the J-functional of logarithmic interpolation spaces (A0, A1) 1, q, A in the category of the p-normed quasi-Banach couples (0 < p ≤ 1). When (A0, A1) is a Banach couple, it is known that the description changes depending on the relationship between q and A. In our more general setting, the parameter p also has an important role as the results show., Ministerio de Economía y Competitividad (MINECO)/FEDER, Ministerio de Educación y Ciencia (MEC), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, inpress

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., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

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., US-Spain Joint Committee for Cultural and Educational Cooperation, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We continue the research on reiteration results between interpolation methods associated to polygons and the. real method. Applications are given to N-tuples of function spaces, or spaces or hounded linear operators and Banach algebras., Spanish Ministerio de Educación y Ciencia, CAM-UCM, RTM PHD, FP6-511953, Departament d’Universitats, Recerca i Societat de la Informació()., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We 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 lattices, DGICYT, French-Spanish cooperation programme Picasso, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We give a maximal description in the sense of Aronszajn-Gagliardo for the real method in the category of quasi-Banach spaces., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

Monográfico: Perspectivas en Análisis Matemático, We investigate the interplay between the different kinds of symmetry that a trihnear form may have and the behaviour of its norm., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We work with Triebel–Lizorkin spaces FsqLp,r(Rn) and Besov spaces BsqLp,r(Rn) with Lorentz smoothness. Using their characterizations by real interpolation we show how to transfer a number of properties of the usual Triebel–Lizorkin and Besov spaces to the spaces with Lorentz smoothness. In particular, we give results on diffeomorphisms, extension operators, multipliers and we also show sufficient conditions on parameters for FsqLp,r(Rn) and BsqLp,r(Rn) to be multiplication algebras., Ministerio de Ciencia e Innovación (MICINN)/FEDER, Ministerio de Educación, Cultura y Deporte, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, FALSE, pub

We characterize compact operators between complex interpolation spaces and between spaces obtained by using certain minimal methods in the sense of Aronszajn and Gagliardo. Applications to interpolation of compact operators are also given., Spanish Ministerio de Ciencia y Tecnología, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We review the interpolation properties of entropy numbers and the measure of non-compactness. We describe the classical results as well as several very recent results., Spanish Ministerio de Ciencia e Innovación, UCM-BSCH, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Instituto de Matemática Interdisciplinar (IMI), TRUE, pub

CRUE-CSIC (Acuerdos Transformativos 2022), We show a necessary and sufficient condition for weak compactness of bilinear operators interpolated by the real method. This characterization does not hold for interpolated operators by the complex method., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We study the interpolation properties of weakly compact bilinear operators by the real method and also by the complex method. We also study the factorization property of weakly compact bilinear operators through reflexive Banach spaces., Ministerio de Ciencia e Innovación (MICINN), Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

CRUE-CSIC (Acuerdos Transformativos 2021), We establish compactness interpolation results for bilinear operators of convolution type and for operators of product type among quasi-Banach spaces. We do not assume any auxiliary condition on the spaces., Ministerio de Ciencia e Innovación (MICINN), Depto. de Análisis Matemático y Matemática Aplicada, Unidad Docente de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, Fac. de Estudios Estadísticos, TRUE, pub

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 characterize here those intermediate spaces that satisfy the conclusion of Cobos-Peetre result for all operators. We also establish some results on rank-one interpolation spaces., Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

This article deals with K- and J-spaces defined by means of polygons. First we establish some reiteration formulae involving the real method, and then we study the behaviour of weakly compact operators. We also show optimality of the weak compactness results., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

We describe the behavior of ideal variations under interpolation methods associated to polygons., DGES, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub