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arXiv · 2404.04028

$\mathbb R$- and $\mathbb C$-supercyclicity for some classes of operators

Emma D'Aniello·Martina Maiuriello
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Abstract

In the present paper we investigate different variants of supercyclicity, precisely $\mathbb R^+$-, $\mathbb R$- and $\mathbb C$-supercyclicity in the context of composition operators. We characterize $\mathbb R$-supercyclic composition operators on $L^p$, $1 \leq p < \infty$. Then, we turn our attention to dissipative composition operators, and we show that $\mathbb R$- and $\mathbb C$-supercyclicity are equivalent notions in this setting and they have a ``shift-like'' characterization.

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Emma D'Aniello, Martina Maiuriello. 2024-04-05. $\mathbb R$- and $\mathbb C$-supercyclicity for some classes of operators. https://arxiv.org/abs/2404.04028

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