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arXiv · 2307.02271

Hypercyclicity of operators that $\lambda$-commute with the Hardy backward shift

Mohamed Amouch·Fernando León-Saavedra·M. P. Romero de la Rosa
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Abstract

An operator $T$ acting on a separable complex Hilbert space $H$ is said to be hypercyclic if there exists $f\in H$ such that the orbit $\{T^n f:\ n\in \mathbb{N}\}$ is dense in $H$. Godefroy and Shapiro \cite{GoSha} characterized those elements in the commutant of the Hardy backward shift which are hypercyclic. In this paper we study some dynamics properties of operators $X$ that $\lambda$-commute with the Hardy backward shift $B$, that is, $BX=\lambda XB$.

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Mohamed Amouch, Fernando León-Saavedra, M. P. Romero de la Rosa. 2023-07-05. Hypercyclicity of operators that $\lambda$-commute with the Hardy backward shift. https://arxiv.org/abs/2307.02271

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