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arXiv · 2403.17904

Quasi-rigid operators and hyper-recurrence

Manuel Saavedra·Manuel Stadlbauer
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Abstract

We study recurrent operators from a new perspective by introducing the notion of hyper-recurrent operators and establish robust connections with quasi-rigid operators. For example, we prove that a recurrent operator on a separable Banach space is quasi-rigid if and only if it is a linear factor of a hyper-recurrent operator, and show that the quasi-rigid operators found in Costakis, Manoussos and Parissis's work, along with many others, are, in fact, hyper-recurrent operators. Furthermore, we provide a negative answer, using a class of operators introduced by Tapia, to the question by Costakis et al. whether $T \oplus T$ is recurrent whenever $T$ is.

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Manuel Saavedra, Manuel Stadlbauer. 2024-03-26. Quasi-rigid operators and hyper-recurrence. https://arxiv.org/abs/2403.17904

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