The Bishop-Phelps-Bollob\'as property for operators deals with simultaneous approximation of an operator T and a vector x at which T:X→Y nearly attains its norm by an operator F and a vector z, respectively, such that F attains its norm at z. We study the possible estimates from above and from below for parameters that measure the rate of approximation in the Bishop-Phelps-Bollob\'as property for operators for the case of Y having the property β of Lindenstrauss.
@article{arxiv.1704.07095,
title = {Quantitative version of the Bishop-Phelps-Bollob\'as theorem for operators with values in a space with the property $\beta$},
author = {Vladimir Kadets and Mariia Soloviova},
journal= {arXiv preprint arXiv:1704.07095},
year = {2017}
}