This is an announcement for the paper "A Bohl--Bohr--Kadets type theorem characterizing Banach spaces not containing $c_0$" by Balint Farkas. Abstract: We prove that a separable Banach space $E$ does not contain a copy of the space $\co$ of null-sequences if and only if for every doubly power-bounded operator $T$ on $E$ and for every vector $x\in E$ the relative compactness of the sets $\{T^{n+m}x-T^nx: n\in \NN\}$ (for some/all $m\in\NN$, $m\geq 1$) and $\{T^nx:n\in \NN\}$ are equivalent. With the help of the Jacobs--de Leeuw--Glicksberg decomposition of strongly compact semigroups the case of (not necessarily invertible) power-bounded operators is also handled. Archive classification: math.FA Mathematics Subject Classification: 47A99, 46B04, 43A60 Submitted from: farkasb@gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1301.6250 or http://arXiv.org/abs/1301.6250