Displaying similar documents to “Properties of lush spaces and applications to Banach spaces with numerical index 1”

Numerical index of vector-valued function spaces

Miguel Martín, Rafael Payá (2000)

Studia Mathematica

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We show that the numerical index of a c 0 -, l 1 -, or l ∞ -sum of Banach spaces is the infimum of the numerical indices of the summands. Moreover, we prove that the spaces C(K,X) and L 1 ( μ , X ) (K any compact Hausdorff space, μ any positive measure) have the same numerical index as the Banach space X. We also observe that these spaces have the so-called Daugavet property whenever X has the Daugavet property.

Extremely non-complex Banach spaces

Miguel Martín, Javier Merí (2011)

Open Mathematics

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A Banach space X is said to be an extremely non-complex space if the norm equality ∥Id +T 2∥ = 1+∥T 2∥ holds for every bounded linear operator T on X. We show that every extremely non-complex Banach space has positive numerical index, it does not have an unconditional basis and that the infimum of diameters of the slices of its unit ball is positive.

Reflexive spaces and numerical radius attaining operators.

María D. Acosta, M. Ruiz Galán (2000)

Extracta Mathematicae

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In this note we deal with a version of James' Theorem for numerical radius, which was already considered in [4]. First of all, let us recall that this well known classical result states that a Banach space satisfying that all the (bounded and linear) functionals attain the norm, has to be reflexive [16].

Recent progress and open questions on the numerical index of Banach spaces.

Vladimir Kadets, Miguel Martín, Rafael Payá (2006)

RACSAM

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The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.

The numerical radius of Lipschitz operators on Banach spaces

Ruidong Wang (2012)

Studia Mathematica

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We study the numerical radius of Lipschitz operators on Banach spaces. We give its basic properties. Our main result is a characterization of finite-dimensional real Banach spaces with Lipschitz numerical index 1. We also explicitly compute the Lipschitz numerical index of some classical Banach spaces.

Norm attaining and numerical radius attaining operators.

María D. Acosta, Rafael Payá (1989)

Revista Matemática de la Universidad Complutense de Madrid

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In this note we discuss some results on numerical radius attaining operators paralleling earlier results on norm attaining operators. For arbitrary Banach spaces X and Y, the set of (bounded, linear) operators from X to Y whose adjoints attain their norms is norm-dense in the space of all operators. This theorem, due to W. Zizler, improves an earlier result by J. Lindenstrauss on the denseness of operators whose second adjoints attain their norms, and is also related to a recent result...