On linear chaos in the spaces of vanishing and convergent sequences

Abstract

We study the chaoticity of bounded and unbounded weighted backward shifts in the space $c_0(\mathbb{N})$ of vanishing sequences via a novel straightforward approach based on a newly found sufficient condition for linear chaos and show that their extensions to the space $c(\mathbb{N})$ of convergent sequences are not even hypercyclic. Thus, we furnish bounded and unbounded linear chaotic operators in $c(\mathbb{N})$ in a different way: as conjugates to the weighted backward shifts in $c_0(\mathbb{Z}_+)$ via a homeomorphic isomorphism between the two spaces.