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

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

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