The Bishop-Phelps-Bollobás property for numerical radius in ${\ell }_1(\mathbb{C})$

Abstract

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 ${\ell }_1(\mathbb{C})$ or $c_0(\mathbb{C})$. As an essential tool we provide two constructive versions of the classical Bishop-Phelps-Bollobás theorem for ${\ell }_1(\mathbb{C})$.

References in corpus (1)

• Recent progress and open questions on the numerical index of Banach spaces