This is an announcement for the paper "The Bishop-Phelps-Bollob'as property for numerical radius in $\ell_1(\mathbb{C})$" by Antonio J. Guirao and Olena Kozhushkina.

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

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 47A12

Submitted from: okozhush@math.kent.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1301.4574

or

http://arXiv.org/abs/1301.4574