Calderon weights and the real interpolation method.
We introduce a class of weights for a which a rich theory of real interpolation can be developed. In particular it led us to extend the commutator theorems associated to this method.
Capacitary Orlicz spaces, Calderón products and interpolation
These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures of the Orlicz function spaces. The goal is to study some aspects of the classical theory of Orlicz spaces for these spaces including the classical theory of interpolation.
Characterization of interpolation spaces and regularity properties for holomorphis semigroups.
Clarkson--McCarthy interpolated inequalities in Finsler norms.
Closed operator ideals and limiting real interpolation
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.
Commutators in real interpolation with quasi-power parameters.
Compact operators between K- and J-spaces
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.
Complex interpolation and property.
Complex interpolation and spaces
Complex interpolation functors with a family of quasi-power function parameters
For the complex interpolation functors associated with derivatives of analytic functions, the Calderón fundamental inequality is formulated in both additive and multiplicative forms; discretization, reiteration, the Calderón-Lozanovskiĭ construction for Banach lattices, and the Aronszajn-Gagliardo construction concerning minimality and maximality are presented. These more general complex interpolation functors are closely connected with the real and other interpolation functors via function parameters...
Composition of (E,2)-summing operators
The Banach operator ideal of (q,2)-summing operators plays a fundamental role within the theory of s-number and eigenvalue distribution of Riesz operators in Banach spaces. A key result in this context is a composition formula for such operators due to H. König, J. R. Retherford and N. Tomczak-Jaegermann. Based on abstract interpolation theory, we prove a variant of this result for (E,2)-summing operators, E a symmetric Banach sequence space.
Construction of a natural norm for the convection-diffusion-reaction operator
In this work, we construct, by means of the function space interpolation theory, a natural norm for a generic linear coercive and non-symmetric operator. We look for a norm which is the counterpart of the energy norm for symmetric operators. The natural norm allows for continuity and inf-sup conditions independent of the operator. Particularly we consider the convection-diffusion-reaction operator, for which we obtain continuity and inf-sup conditions that are uniform with respect to the operator...
Convergence of Taylor series in Hardy and Besov spaces.
Copies of Orlicz sequences spaces in the interpolation spaces .
Corrigendum on the paper Remarks on compact operators between interpolation spaces associated to polygons.
Here are given the figures of this paper, initially published with some omissions.
Dual Banach algebras: representations and injectivity
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments....
Dual results of factorization for operators.
Eigenvalue distribution of integral operators defined by Besov-Orlicz kernels.
Eigenvalue distribution of integral operators defined by Orlicz kernels.
Embedding functions and their role in interpolation theory.