On the Bishop-Phelps-Bollobas Property for Numerical Radius

초록

We study the Bishop-Phelps-Bollobas 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 (mu)-spaces have this property for every measure mu. 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-Nikodym property (even reflexivity) is not enough to get BPBp-nu.

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