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arXiv · 2203.02032

On linear chaos in the spaces of vanishing and convergent sequences

Marat V. Markin·Gabriel Martinez Lazaro·Edward S. Sichel
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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.

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Marat V. Markin, Gabriel Martinez Lazaro, Edward S. Sichel. 2022-03-03. On linear chaos in the spaces of vanishing and convergent sequences. https://arxiv.org/abs/2203.02032

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