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arXiv · 1708.08690

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

M. D. Acosta·M. Fakhar·M. Soleimani-Mourchehkhorti
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Abstract

In this paper, we introduce the notion of the Bishop-Phelps-Bollob\'as 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-$\nu$.

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BibTeXRIS

M. D. Acosta, M. Fakhar, M. Soleimani-Mourchehkhorti. 2017-08-29. The Bishop-Phelps-Bollob{\'a}s property for numerical radius of operators on $L_1 (\mu)$. https://doi.org/10.1016/j.jmaa.2017.08.060

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