This is an announcement for the paper “Quantitative version of the Bishop-Phelps-Bollobás theorem for operators with values in a space with the property $\beta$” by Vladimir Kadetshttps://arxiv.org/find/math/1/au:+Kadets_V/0/1/0/all/0/1, Mariia Soloviovahttps://arxiv.org/find/math/1/au:+Soloviova_M/0/1/0/all/0/1.

Abstract: The Bishop-Phelps-Bollob'as property for operators deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T: X\rightarrow Y$ 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 $\beta$ of Lindenstrauss.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1704.07095