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

TL;DR

This paper characterizes necessary and sufficient conditions for the boundedness and local boundedness of composition operators acting on sequence spaces of bounded variation, specifically in $bv_p(E)$ spaces.

Contribution

It provides a comprehensive characterization of acting conditions and boundedness for composition operators in $bv_p(E)$ spaces, extending understanding in sequence space operator theory.

Findings

Necessary and sufficient conditions for acting of composition operators

Characterization of boundedness and local boundedness

Results applicable to $bv_p(E)$ spaces for $p \\geq 1$

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.