Georgia Institute of Technology College of Sciences

The Bishop-Phelps-Bolloba ́s property for numerical radius says that if we have a point in the Banach space and an operator that almost attains its numerical radius at this point, then there exist another point close to the original point and another operator close to the original operator, such that the new operator attains its numerical radius at this new point. We will show that the set of bounded linear operators from a Banach space X to X has a Bishop-Phelps-Bolloba ́s property for numerical radius whenever X is l1 or c0. We will also discuss some constructive versions of the Bishop-Phelps- Bolloba ́s theorem for l1(C), which are an essential tool for the proof of this result.