On some Fréchet interpolation spaces.

Jesús M. Fernández Castillo

Displaying similar documents to “On some Fréchet interpolation spaces.”

Fréchet interpolation spaces and Grothendieck operator ideals.

Jesús M. Fernández Castillo (1991)

Collectanea Mathematica

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Starting with a continuous injection I: X → Y between Banach spaces, we are interested in the Fréchet (non Banach) space obtained as the reduced projective limit of the real interpolation spaces. We study relationships among the pertenence of I to an operator ideal and the pertenence of the given interpolation space to the Grothendieck class generated by that ideal.

Interpolation of compact operators by Goulaouic procedure

Fernando Cobos (1990)

Studia Mathematica

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On interpolation of tensor products of Banach spaces.

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.

Interpolation theory and measures related to operator ideals

Cobos, Fernando

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Given any operator ideal $ℐ$ , there are two natural functionals $γ_{ℐ} (T)$ , $β_{ℐ} (T)$ that one can use to show the deviation of the operator $T$ to the closed surjective hull of $ℐ$ and to the closed injective hull of $ℐ$ , respectively. We describe the behaviour under interpolation of $γ_{ℐ}$ and $β_{ℐ}$ . The results are part of joint works with A. Martínez, A. Manzano and P. Fernández-Martínez.

Remarks on compact operators between interpolation spaces associated to polygons.

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.

Real interpolation and compactness.

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.

Factoring weakly compact homomorphisms, interpolation of Banach algebras and multilinear interpolation

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.

On the relation between complex and real methods of interpolation

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.

A commutator theorem with applications.

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...