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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
We investigate compact operators between approximation spaces, paying special attention to the limit case. Applications are given to embeddings between Besov spaces.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
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
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.texto impreso
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 [...]texto impreso
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.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 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 redu[...]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
Cobos, Fernando ; Fernández-Martínez, Pedro ; Martínez, Antón ; Raynaud, Yves | Cambridge Univ Press | 1999We 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 f[...]texto impreso
We study the interpolation properties of Asplund operators by the complex method, as well as by general J - and K-methods.
