The Bishop–Phelps–Bollobás property for numerical radius in $\ell _{1}(\mathbb {C})$
Volume 218 / 2013
Studia Mathematica 218 (2013), 41-54
MSC: 47A12, 46B28.
DOI: 10.4064/sm218-1-3
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 $\ell _1(\mathbb {C})$.
