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<p>This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators <i>T</i> in the case were the dual <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43036_2025_437_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(T^*\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>T</mi> <mo>∗</mo> </msup> </math></EquationSource> </InlineEquation> has empty point spectrum.</p>

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On the spectrum of supercyclic/hypercyclic operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月30日

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  • Pietro Aiena,
  • Fabio Burderi,
  • Salvatore Triolo

摘要

This paper concerns the spectral structure of hypercyclic and supercyclic operators defined on Banach spaces, or defined on Hilbert spaces. We also consider the spectral properties of operators in Hilbert spaces that commute with a hypercyclic operator. A result of Herrero and Kitai (Proc Am Math Soc 116(3):873–875, 1992) is extended to Drazin invertible operators. In particular, a Drazin invertible operator is hypercyclic if and only if is invertible. An analogous result holds for supercyclic operators T in the case were the dual \(T^*\) T ∗ has empty point spectrum.