  The aim of this paper is to give the answer to the problem of
characterization of acting conditions (necessary as well as sufficient) for
composition operators in some sequence spaces. We also characterize their
boundedness and local boundedness. We focus on composition operators acting to
or from the space $bv_p(E)$ of all sequences of $p$-bounded variation; here
$p\geq 1$ and $E$ is a normed space.
