Type: Article
The Bishop–Phelps–Bollobás property for numerical radius of operators on L1(μ)
Journal: Journal of Mathematical Analysis and Applications (0022247X)Year: 2018Volume: Issue: 2Pages: 925 - 936
All Open Access; Bronze Open Access; Green Open AccessDOI:10.1016/j.jmaa.2017.08.060Language: English
Abstract
In this paper, we introduce the notion of the Bishop–Phelps–Bollobás property for numerical radius (BPBp-ν) for a subclass of the space of bounded linear operators. Then, we show that certain subspaces of L(L1(μ)) have the BPBp-ν for every finite measure μ. As a consequence we deduce that the subspaces of finite-rank operators, compact operators and weakly compact operators on L1(μ) have the BPBp-ν. © 2017 Elsevier Inc.
Author Keywords
Banach spaceBishop–Phelps–Bollobás propertyBishop–Phelps–Bollobás theoremNumerical radius attaining operator