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On the Compact Operators Case of the Bishop–Phelps–Bollobás Property for Numerical Radius
Results in Mathematics ( IF 1.1 ) Pub Date : 2021-05-26 , DOI: 10.1007/s00025-021-01430-5
Domingo García , Manuel Maestre , Miguel Martín , Óscar Roldán

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.



中文翻译:

关于Bishop–Phelps–Bollobás属性的数值半径的紧凑型算子

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。

更新日期:2021-05-26
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