Displaying similar documents to “Numerical index of vector-valued function spaces”

Properties of lush spaces and applications to Banach spaces with numerical index 1

Kostyantyn Boyko, Vladimir Kadets, Miguel Martín, Javier Merí (2009)

Studia Mathematica

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The concept of lushness, introduced recently, is a Banach space property, which ensures that the space has numerical index 1. We prove that for Asplund spaces lushness is actually equivalent to having numerical index 1. We prove that every separable Banach space containing an isomorphic copy of c₀ can be renormed equivalently to be lush, and thus to have numerical index 1. The rest of the paper is devoted to the study of lushness just as a property of Banach spaces. We prove that lushness...

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].

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...

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.