We establish interpolation properties under limiting real methods for a class of closed ideals including weakly compact operators, Banach-Saks operators, Rosenthal operators and Asplund operators. We show that they behave much better than compact operators.
We 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.
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.
This note deals with interpolation methods defined by means of polygons. We show necessary and sufficient conditions for compactness of operators acting from a J-space into a K-space.
We investigate inclusion indices for quasi-Banach spaces. First we consider the case of function spaces on , then the sequence case and finally we develop an abstract approach dealing with indices defined by the real interpolation scale gen- erated by a quasi-Banach couple.
This paper deals with the following problem: Let T be a given operator. Find conditions on v(x) (resp. u(x)) such that ∫ |Tf(x)|pu(x) dx ≤ C ∫ |f(x)|pv(x) dx is satisfied for some u(x) (resp. v(x)). Using vector-valued inequalities the problem is solved for: Carleson's maximal operator of Fourier partial sums, Littlewood-Paley square functions, Hilbert transform of functions valued in...
Here are given the figures of this paper, initially published with some omissions.
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