The Bishop–Phelps–Bollobás property for numerical radius in l₁(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 v