On the Bishop-Phelps-Bollobás Property for Numerical Radius

الملخص EN

We study the Bishop-Phelps-Bollobás property for numerical radius (in short, BPBp-nu) and find sufficient conditions for Banach spaces to ensure the BPBp-nu.

Among other results, we show that L 1 μ -spaces have this property for every measure μ.

On the other hand, we show that every infinite-dimensional separable Banach space can be renormed to fail the BPBp-nu.

In particular, this shows that the Radon-Nikodým property (even reflexivity) is not enough to get BPBp-nu.