A Dense Lineability Criterion for Linear Dynamics

Abstract We introduce and study Li-Yorke chaos for sequences of continuous linear operators from an $$F$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>F</mml:mi> </mml:math> -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 $$\textrm{D}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>D</mml:mtext> </mml:math> -phenomenon to establish a common dense lineability criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos.