Composition operators in $bv_p$-spaces, part I: acting conditions and boundedness

Abstract

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.