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

Antonio J. Guirao, Olena Kozhushkina

Published 2013-01-19Version 1

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 $\ell_1(\mathbb{C})$.