Introduces a dense lineability criterion for linear dynamics, highlighting chaotic behavior in Banach spaces, suggesting new insights into operator theory.
We introduce and study Li-Yorke chaos for sequences of continuous linear operators from an F F -space to a normed space. 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. We introduce the D D -phenomenon to establish a common dense lineability criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos.
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Arbieto et al. (2026) studied this question.
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