On the compact operators case of the Bishop-Phelps-Bollobás property for numerical radius García, Domingo Maestre, Manuel Martín Suárez, Miguel Roldán, Óscar The authors would like to thank Bill Johnson for kindly answering several inquiries. We study the Bishop–Phelps–Bollobás property for numerical radius restricted to the case of compact operators (BPBp-nu for compact operators in short). We show that C0(L) spaces have the BPBp-nu for compact operators for every Hausdorff topological locally compact space L. To this end, on the one hand, we provide some techniques allowing to pass the BPBp-nu for compact operators from subspaces to the whole space and, on the other hand, we prove some strong approximation property of C0(L) spaces and their duals. Besides, we also show that real Hilbert spaces and isometric preduals of ℓ1 have the BPBp-nu for compact operators. 2021-06-17T10:09:39Z 2021-06-17T10:09:39Z 2021-02-22 info:eu-repo/semantics/article Publisher version: García, D., Maestre, M., Martín, M. et al. On the Compact Operators Case of the Bishop–Phelps–Bollobás Property for Numerical Radius. Results Math 76, 122 (2021). [https://doi.org/10.1007/s00025-021-01430-5] http://hdl.handle.net/10481/69256 10.1007/s00025-021-01430-5 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Springer Nature