Fernando Cobos Díaz (1989)
Revista Matemática de la Universidad Complutense de Madrid
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The behavior of compactness under real interpolation real is discussed. Classical results due to Krasnoselskii, Lions-Peetre, Persson, and Hayakawa are described, as well as others obtained very recently by Edmunds, Potter, Fernández, and the author.
D. Staszak (1992)
Collectanea Mathematica
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Mieczysław Mastyło, Vladimir Ovchinnikov (1997)
Studia Mathematica
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We study those compatible couples of Banach spaces for which the complex method interpolation spaces are also described by the K-method of interpolation. As an application we present counter-examples to Cwikel's conjecture that all interpolation spaces of a Banach couple are described by the K-method whenever all complex interpolation spaces have this property.
Fernando Cobos, Luz M. Fernández-Cabrera (2008)
Banach Center Publications
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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.
Pustylnik, Evgeniy (1996)
Abstract and Applied Analysis
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Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez (2006)
RACSAM
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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.
Mario Milman (1993)
Collectanea Mathematica
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We give an extension of the commutator theorems of Jawerth, Rochberg and Weiss [9] for the real method of interpolation. The results are motivated by recent work by Iwaniek and Sbordone [6] on generalized Hodge decompositions. The main estimates of these authors are based on a commutator theorem for a specific operator acting on Lp spaces and through the use of the complex method of interpolation. In this note we give an extension of the Iwaniek-Sbordone theorem to general real interpolation...
Andreas Defant, Mieczyslaw Mastylo, Carsten Michels (2003)
RACSAM
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For the complex interpolation method, Kouba proved an important interpolation formula for tensor products of Banach spaces. We give a partial extension of this formula in the injective case for the Gustavsson?Peetre method of interpolation within the setting of Banach function spaces.
Mieczysław Mastylo (1991)
Studia Mathematica
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María J. Carro (1994)
Collectanea Mathematica
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Maria Carro (1994)
Studia Mathematica
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We develop a new method of real interpolation for infinite families of Banach spaces that covers the methods of Lions-Peetre, Sparr for N spaces, Fernández for spaces and the recent method of Cobos-Peetre.
L. Maligranda, L. E. Persson (1993)
Collectanea Mathematica
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Some examples of the close interaction between inequalities and interpolation are presented and discussed. An interpolation technique to prove generalized Clarkson inequalities is pointed out. We also discuss and apply to the theory of interpolation the recently found facts that the Gustavsson-Peetre class P can be described by one Carlson type inequality and that the wider class P can be characterized by another Carlson type inequality with blocks.