Displaying similar documents to “Absolutely (r,p,q)-summing inclusions”

On the Schatten S classes.

Marilda A. Simôes (1991)

Extracta Mathematicae

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The Schatten Sp classes, 1 ≤ p ≤ ∞, were introduced and studied in [6] in connection with the problem of finding suitable classes of operators having a well-defined trace. In this paper we consider a generalization Sφ of the Schatten classes Sp obtained in correspondence with opportune, continuous, strictly increasing, sub-additive functions φ: [0,∞) → [0,∞) such that φ(0) = 0 and φ(1) = 1. Our purpose is to study...

The inclusion theorem for multiple summing operators

David Pérez-García (2004)

Studia Mathematica

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We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.

Finite representability and super-ideals of operators

Stefan Heinrich

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CONTENTSIntroduction............................................................................... 5Notation............................................................................................. 61. Finite representability of operators.......................................... 72. Super-ideals of operators......................................................... 143. Connections with Banach space theory................................. 204. Procedures on super-ideals........................................................

Closed operator ideals and limiting real interpolation

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

Studia Mathematica

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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.

On the space of φ-nuclear operators on l.

Marilda A. Simoes (1990)

Collectanea Mathematica

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We consider the generalization Sphi of the Schatten classes Sp obtained in correspondence with opportune continuous, strictly increasing, sub-additive functions phi such that phi(0) = 0 and phi(1) = 1. The purpose of this note is to study the spaces Sphi of the phi-nuclear operators and to compare their properties to those of the by now well-known space S1 of nuclear operators.

On multilinear generalizations of the concept of nuclear operators

Dahmane Achour, Ahlem Alouani (2010)

Colloquium Mathematicae

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This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞ ) m-linear...