Daugavet centers are separably determined - T. Ivashyna (Математичні Студії)
A linear bounded operator $G$ acting from a~Banach space $X$ intoa~Banach space $Y$ is a~Daugavet center if every linear boundedrank-$1$ operator $Tcolon X o Y$ fulfills$|G+T|=|G|+|T|$. We prove that $G colon X o Y$is a~Daugavet center if and only if for every separable subspaces$X_1subset X$ and $Y_1subset Y$ there exist separable subspaces$X_2subset X$ and $Y_2subset Y$ such that $X_1subset X_2$,$Y_1subset Y_2$, $G(X_2)subset Y_2$ and the restriction$G|_{X_2} colon X_2 o Y_2$ of $G$ is a~Daugavetcenter. We apply this fact to study the set of $G$-narrowoperators.