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arXiv · 2107.12103

Shift-like Operators on $L^p(X)$

Emma D'Aniello·Udayan B. Darji·Martina Maiuriello
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Abstract

In this article we develop a general technique which takes a known characterization of a property for weighted backward shifts and lifts it up to a characterization of that property for a large class of operators on $L^p(X)$. We call these operators ``shift-like''. The properties of interest include chaotic properties such as Li-Yorke chaos, hypercyclicity, frequent hypercyclicity as well as properties related to hyperbolic dynamics such as shadowing, expansivity and generalized hyperbolicity. Shift-like operators appear naturally as composition operators on $L^p(X)$ when the underlying space is a dissipative measure system. In the process of proving the main theorem, we provide some results concerning when a property is shared by a linear dynamical system and its factors.

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Emma D'Aniello, Udayan B. Darji, Martina Maiuriello. 2021-07-26. Shift-like Operators on $L^p(X)$. https://arxiv.org/abs/2107.12103

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