On the Bishop-Phelps-Bollobás Property for Numerical Radius Kim, Sun Kwang Lee, Han Ju Martín Suárez, Miguel Attaining operators Holomorphic functions Spaces Polynomials Denseness Index Norm 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 -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. 2014-05-23T11:18:47Z 2014-05-23T11:18:47Z 2014 journal article Kim, S.K.; Lee, H.J.; Martín, M. On the Bishop-Phelps-Bollobás Property for Numerical Radius. Abstract and Applied Analysis, 2014: 479208 (2014). [http://hdl.handle.net/10481/31887] 1085-3375 1687-0409 http://hdl.handle.net/10481/31887 10.1155/2014/479208 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ open access Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Hindawi Publishing Corporation