<p>We introduce and study Li-Yorke chaos for sequences of continuous linear operators from an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>F</mi> </math></EquationSource> </InlineEquation>-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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textrm{D}\)</EquationSource> <EquationSource Format="MATHML"><math> <mtext>D</mtext> </math></EquationSource> </InlineEquation><i>-phenomenon</i> to establish a common dense lineability criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos.</p>

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A Dense Lineability Criterion for Linear Dynamics

  • Alexander Arbieto,
  • Manuel Saavedra

摘要

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 \(\textrm{D}\) D -phenomenon to establish a common dense lineability criterion that encompasses properties such as recurrence, universality, and Li-Yorke chaos.