Displaying similar documents to “Reflexive spaces and numerical radius attaining operators.”

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.

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...

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...

The Bishop-Phelps-Bollobás property for numerical radius in ℓ₁(ℂ)

Antonio J. Guirao, Olena Kozhushkina (2013)

Studia Mathematica

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We show that the set of bounded linear operators from X to X admits a Bishop-Phelps-Bollobás type theorem for numerical radius whenever X is ℓ₁(ℂ) or c₀(ℂ). As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ℓ₁(ℂ).

Numerical index with respect to an operator

Mohammad Ali Ardalani (2014)

Studia Mathematica

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We introduce new concepts of numerical range and numerical radius of one operator with respect to another one, which generalize in a natural way the known concepts of numerical range and numerical radius. We study basic properties of these new concepts and present some examples.