Displaying similar documents to “The Bishop-Phelps-Bollobás property for numerical radius in 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.

On upper and lower bounds of the numerical radius and an equality condition

Takeaki Yamazaki (2007)

Studia Mathematica

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We give an inequality relating the operator norm of T and the numerical radii of T and its Aluthge transform. It is a more precise estimate of the numerical radius than Kittaneh's result [Studia Math. 158 (2003)]. Then we obtain an equivalent condition for the numerical radius to be equal to half the operator norm.

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...

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].