Quantitative version of the Bishop-Phelps-Bollobas theorem for operators with values in a space with the property $\beta$

V. Kadets, M. Soloviova
School of Mathematics and Informatics; Kharkiv V.N. Karazin National University, Kharkiv, Ukraine
The Bishop-Phelps-Bollobas property for operators deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T\colon X\rightarrow Y$ 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-Bollobas property for operators for the case of $Y$ having the property $\beta$ of Lindenstrauss.
Bishop-Phelps-Bollobas theorem; norm-attaining operators; property $\beta$ of Lindenstrauss
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