The Bishop-Phelps-Bollobás property for numerical radius of operators on L1(μ)

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.