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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.

Caractérisation Des Espaces 1-Matriciellement Normés

Le Merdy, Christian, Mezrag, Lahcéne (2002)

Serdica Mathematical Journal

Let X be a closed subspace of B(H) for some Hilbert space H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] = (S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X) and showed that there are p−matricially normed spaces. In this paper we prove that conversely, if X is a p−matricially normed space with p = 1, then there is an operator structure on X, such that M1,n (X) = S1 [X] where Sn,1 [X] is the finite dimentional version of S1 [X]. For p...

Characterization of some interpolation spaces (I)

Alessandra Lunardi (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si calcolano alcuni spazi di interpolazione fra spazi di funzioni hölderiane.

Characterization of some interpolation spaces (II)

Alessandra Lunardi (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si caratterizzano alcuni spazi di interpolazione tra spazi di funzioni continue e domini di operatori ellittici del 2° ordine.

Characterization of strict C*-algebras

O. Aristov (1994)

Studia Mathematica

A Banach algebra A is called strict if the product morphism is continuous with respect to the weak norm in A ⊗ A. The following result is proved: A C*-algebra is strict if and only if all its irreducible representations are finite-dimensional and their dimensions are bounded.

Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives

Paweł Domański (2004)

Banach Center Publications

This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...

Coactions and fell bundles.

Kaliszewski, S., Muhly, Paul S., Quigg, John, Williams, Dana P. (2010)

The New York Journal of Mathematics [electronic only]

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