On linear chaos in the space of convergent sequences

Abstract: We show that linear chaos in the space $c(\mathbb{N})$ of convergent sequences cannot be arrived at by merely extending the weighted backward shifts in the space $c_0(\mathbb{N})$ of vanishing sequences. Applying a newly found sufficient condition for linear chaos, we furnish concise proofs of the chaoticity of the foregoing operators along with their powers and also itemize their spectral structure. We further construct bounded and unbounded linear chaotic operators in $c(\mathbb{N})$ as conjugate to the chaotic backward shifts in $c_0(\mathbb{Z}_+)$ via a homeomorphic isomorphism between the two spaces.