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arXiv · 2502.03352

Dense Lineable Criterion for Linear Dynamics

Alexander Arbieto·Manuel Saavedra
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Abstract

We study Li-Yorke chaos for sequences of continuous linear operators from an \(F\)-space to a normed space. We introduce the \emph{D-phenomenon} to establish a common dense lineable criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos. We show that in every infinite-dimensional separable complex Banach space, there exists a sequence of operators with a dense set of irregular vectors but without a dense irregular manifold, and we exhibit a recurrent operator whose set of recurrent vectors is not dense-lineable. This resolves in the negative a question posed by Grivaux et al.

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Alexander Arbieto, Manuel Saavedra. 2025-02-05. Dense Lineable Criterion for Linear Dynamics. https://arxiv.org/abs/2502.03352

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