Displaying similar documents to “Narrow operators and rich subspaces of Banach spaces with the Daugavet property”

Lineability of functionals and operators

Francisco Javier García-Pacheco, Daniele Puglisi (2010)

Studia Mathematica

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This article is divided into two parts. The first one is on the linear structure of the set of norm-attaining functionals on a Banach space. We prove that every Banach space that admits an infinite-dimensional separable quotient can be equivalently renormed so that the set of norm-attaining functionals contains an infinite-dimensional vector subspace. This partially solves a question proposed by Aron and Gurariy. The second part is on the linear structure of dominated operators. We show...

Composition of (E,2)-summing operators

Andreas Defant, Mieczysław Mastyło (2003)

Studia Mathematica

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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.

On the norm of a projection onto the space of compact operators

Joosep Lippus, Eve Oja (2007)

Studia Mathematica

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Let X and Y be Banach spaces and let 𝓐(X,Y) be a closed subspace of 𝓛(X,Y), the Banach space of bounded linear operators from X to Y, containing the subspace 𝒦(X,Y) of compact operators. We prove that if Y has the metric compact approximation property and a certain geometric property M*(a,B,c), where a,c ≥ 0 and B is a compact set of scalars (Kalton's property (M*) = M*(1, {-1}, 1)), and if 𝓐(X,Y) ≠ 𝒦(X,Y), then there is no projection from 𝓐(X,Y) onto 𝒦(X,Y) with norm less than...

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.

On operators close to isometries

Sameer Chavan (2008)

Studia Mathematica

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We introduce and discuss a class of operators, to be referred to as operators close to isometries. The Bergman-type operators, 2-hyperexpansions, expansive p-isometries, and certain alternating hyperexpansions are main examples of such operators. We establish a few decomposition theorems for operators close to isometries. Applications are given to the theory of p-isometries and of hyperexpansive operators.