The Bishop-Phelps-Bollob{á}s property for numerical radius of operators on $L_1(\mu )$

Abstract

In this paper, we introduce the notion of the Bishop-Phelps-Bollobás property for numerical radius (BPBp-$\nu$) for a subclass of the space of bounded linear operators. Then, we show that certain subspaces of $\mathcal{L}(L_1(\mu ))$ have the BPBp-$\nu$ for every finite measure $\mu$. As a consequence we deduce that the subspaces of finite-rank operators, compact operators and weakly compact operators on $L_1(\mu )$ have the BPBp-$\nu$.

15 pages

Cited by in corpus (1)

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