The Bishop-Phelps-Bollob\'as property for numerical radius in $\ell_1(\mathbb{C})$

Antonio J. Guirao; Olena Kozhushkina

The Bishop-Phelps-Bollob\'as property for numerical radius in $\ell_1(\mathbb{C})$

Functional Analysis 2013-01-22 v1

Authors: Antonio J. Guirao , Olena Kozhushkina

Abstract

We show that the set of bounded linear operators from $X$ to $X$ admits a Bishop-Phelps-Bollob\'as type theorem for numerical radius whenever $X$ is $\ell_1(\mathbb{C})$ or $c_0(\mathbb{C})$ . As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollob\'as theorem for $\ell_1(\mathbb{C})$ .

Keywords

Bishop-Phelps-Bollobás property numerical radius bounded linear operators Banach spaces

Cite

@article{arxiv.1301.4574,
  title  = {The Bishop-Phelps-Bollob\'as property for numerical radius in $\ell_1(\mathbb{C})$},
  author = {Antonio J. Guirao and Olena Kozhushkina},
  journal= {arXiv preprint arXiv:1301.4574},
  year   = {2013}
}

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