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Calderón couples of rearrangement invariant spaces

N. Kalton (1993)

Studia Mathematica

We examine conditions under which a pair of rearrangement invariant function spaces on [0,1] or [0,∞) form a Calderón couple. A very general criterion is developed to determine whether such a pair is a Calderón couple, with numerous applications. We give, for example, a complete classification of those spaces X which form a Calderón couple with L ∞ . We specialize our results to Orlicz spaces and are able to give necessary and sufficient conditions on an Orlicz function F so that the pair ( L F , L ∞ ) forms a...

Calderon weights and the real interpolation method.

J. Bastero, M. Milman, F. J. Ruiz (1996)

Revista Matemática de la Universidad Complutense de Madrid

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

Pilar Silvestre (2014)

Banach Center Publications

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.

Closed operator ideals and limiting real interpolation

Luz M. Fernández-Cabrera, Antón Martínez (2014)

Studia Mathematica

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.

Compact operators between K- and J-spaces

Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez (2005)

Studia Mathematica

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 functors with a family of quasi-power function parameters

Ming Fan (1994)

Studia Mathematica

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

Andreas Defant, Mieczysław Mastyło (2003)

Studia Mathematica

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

Giancarlo Sangalli (2004)

Bollettino dell'Unione Matematica Italiana

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...

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