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arXiv · 2211.07224

On spaceability of shifts-like operators on $L^p$

Emma D'Aniello·Martina Maiuriello
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Abstract

We prove the spaceability of the set of hypercyclic vectors for {\em shifts-like operators}. Shift-like operators appear naturally as composition operators on $L^p(X)$, when the underlying space $X$ is dissipative. In the process of proving the main theorem, we provide, among other results of independent interest, a characterization of weakly mixing dissipative composition operators of bounded distortion.

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Emma D'Aniello, Martina Maiuriello. 2022-11-14. On spaceability of shifts-like operators on $L^p$. https://doi.org/10.1016/j.jmaa.2023.127177

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