On the Compact Operators Case of the Bishop-Phelps-Bollobas Property for Numerical Radius

被引：1

作者：

Garcia, Domingo ^{[1
]}

Maestre, Manuel ^{[1
]}

Martin, Miguel ^{[2
]}

Roldan, Oscar ^{[1
]}

机构：

[1] Univ Valencia, Dept Analisis Matemat, Doctor Moliner 50, Burjasot Valencia 46100, Spain

[2] Univ Granada, Dept Analisis Matemat, Fac Ciencias, Granada 18071, Spain

来源：

RESULTS IN MATHEMATICS | 2021年 / 76卷 / 03期

关键词：

Banach space; compact operator; Bishop-Phelps-Bollobas property; numerical radius attaining operator; approximation property; Primary; 46B04; Secondary; 46B20; 46B25; 46B28; LINDENSTRAUSS PROPERTIES; VERSION;

D O I：

10.1007/s00025-021-01430-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Bishop-Phelps-Bollobas 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.

引用

页数：23

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