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 \(C_0(L)\) 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 \(C_0(L)\) spaces and their duals. Besides, we also show that real Hilbert spaces and isometric preduals of \(\ell _1\) have the BPBp-nu for compact operators.

我们研究Bishop–Phelps–Bollobás属性的数值半径仅限于紧凑算子（简称为BPBp-nu）。我们证明\（C_0（L）\）空间具有每个Hausdorff拓扑局部紧凑空间L的紧凑算子的BPBp-nu 。为此，一方面，我们提供了一些技术，允许将紧凑算子的BPBp-nu从子空间传递到整个空间，另一方面，我们证明了\（C_0（L）\ ）空间及其对偶。此外，我们还证明了\（\ ell _1 \）的实Hilbert空间和等距前置项具有BPBp-nu用于紧算子。