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<p>Although recurrence for dynamical systems has been studied since the end of the nineteenth century, the study of recurrence for linear operators started with papers by Costakis, Manoussos and Parissis in 2012 and 2014. We explore recurrence in Banach algebras, in the space of continuous linear operators on <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1779_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega =\mathbb {C}^{\mathbb {N}},\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ω</mi> <mo>=</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi mathvariant="double-struck">N</mi> </msup> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> and for composition operators whose symbols are linear fractional transformations, acting on weighted Dirichlet spaces. In particular, we show that composition operators with a parabolic non automorphism symbol are never recurrent.</p>

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Recurrent Operators on Function Spaces

  • 期刊论文

  • 发表日期：

    2025年8月4日

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  • Gabriela Bulancea,
  • Héctor N. Salas

摘要

Although recurrence for dynamical systems has been studied since the end of the nineteenth century, the study of recurrence for linear operators started with papers by Costakis, Manoussos and Parissis in 2012 and 2014. We explore recurrence in Banach algebras, in the space of continuous linear operators on \(\omega =\mathbb {C}^{\mathbb {N}},\) ω = C N , and for composition operators whose symbols are linear fractional transformations, acting on weighted Dirichlet spaces. In particular, we show that composition operators with a parabolic non automorphism symbol are never recurrent.