Archiv der Mathematik

, Volume 112, Issue 6, pp 633–643 | Cite as

Hypercyclic composition operators on the \(S^p \) space with automorphism symbols

  • Shi-An Han
  • Ze-Hua ZhouEmail author


Let \(S^p\) be the space of holomorphic functions whose derivative lies in the classical Hardy space \(H^p\) over the unit disk. We prove in this paper that the composition operator \(C_\varphi \) with \(\varphi \) an automorphism is hypercyclic on \(S^p\), \(0<p<1\), if and only if \(\varphi \) has no interior fixed point. This answers affirmatively a problem posed by Colonna and Martínez-Avendaño in the paper “Hypercyclicity of composition operators on Banach spaces of analytic functions” (Complex Anal Oper Theory 12(1): 305–323, 2018).


Composition operator Hypercyclic \(S^p\) space Automorphism 

Mathematics Subject Classification

47A16 47B33 47B38 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of ScienceCivil Aviation University University of ChinaTianjinPeople’s Republic of China
  2. 2.School of MathematicsTianjin UniversityTianjinPeople’s Republic of China

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