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A procedure is given to reduce the interpolation spaces on an ordered pair generated by the function parameter t? (1 + |log t|)?b to the classical real interpolation spaces. Applications are given for Lorentz–Zygmund function spaces, Besov space[...]texto impreso
We establish a formula for the measure of non-compactness of an operator interpolated by the general real method generated by a sequence lattice ?. The formula is given in terms of the norms of the shift operators in ?.texto impreso
Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Polish Acad Sciencies Inst Mathematics | 2005The 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 a[...]texto impreso
We establish a compactness interpolation result for bilinear operators of the type proved by Janson for bounded bilinear operators. We also give an application to compactness of convolution operators.texto impreso
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.texto impreso
Cobos, Fernando ; Fernández-Cabrera, Luz M. | 2020We review several results on duality of logarithmic interpolation spaces and applications to Besov spaces. We also establish some new results on Besov spaces with smoothness close to zero defined by differences.texto impreso
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.texto impreso
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.texto impreso
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.texto impreso
Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Manzano, Antonio ; Martínez, Antón | Heldermann Verlag | 2007Let 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[...]texto impreso
We establish formulae for the measure of non-compactness of operators interpolated by limiting methods that come up by the choice ?=0 and ?=1 in the definition of the real method.texto impreso
Let ? = (A? , A?) , B? = (B? , B?) be Banach couples, let E be a Banach space and let T be a bilinear operator such that ||T(a, b)||? ? M[sub]j ||a||?[sub]j ||b||?[sub]j for a ? A? ? A?, b ? B? ? B?, j = 0, 1. If T : A°[sub]j × B°[sub]j ?? E com[...]texto impreso
We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.texto impreso
Cobos, Fernando ; Fernández-Cabrera, Luz M. ; Martínez, Antón | Gauthier-Villars/Editions Elsevier | 2006We show a necessary and sufficient condition on the lattice ? for the general real method (· , ·)? to preserve the Banach-algebra structure. As an application we derive factorization of weakly compact homomorphisms through interpolation properti[...]texto impreso
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.
