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On S. Grivaux’ example of a hypercyclic rank one perturbation of a unitary operator


Recently, Sophie Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. We give a similar construction using a functional model for rank one perturbations of singular unitary operators.

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Correspondence to Anton Baranov.

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The authors were supported by the Chebyshev Laboratory (St. Petersburg State University) under RF Government Grant 11.G34.31.0026, by JSC “Gazprom Neft” and by the Grant MD-5758.2015.1. A. Baranov was supported by Dmitry Zimin’s Dynasty Foundation. A. Lishanskii was supported by RFBR Grant 14-01-31163.

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Baranov, A., Lishanskii, A. On S. Grivaux’ example of a hypercyclic rank one perturbation of a unitary operator. Arch. Math. 104, 223–235 (2015).

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Mathematics Subject Classification

  • 47A16
  • 30A76
  • 30H10


  • Hypercyclic operator
  • Rank one perturbation
  • Inner function
  • Model space
  • Functional model