Displaying similar documents to “Numerical radius attaining operators.”

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...

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).

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].

A class of tridiagonal operators associated to some subshifts

Christian Hernández-Becerra, Benjamín A. Itzá-Ortiz (2016)

Open Mathematics

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We consider a class of tridiagonal operators induced by not necessary pseudoergodic biinfinite sequences. Using only elementary techniques we prove that the numerical range of such operators is contained in the convex hull of the union of the numerical ranges of the operators corresponding to the constant biinfinite sequences; whilst the other inclusion is shown to hold when the constant sequences belong to the subshift generated by the given biinfinite sequence. Applying recent results...

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.