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

Abstract

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.

Additional information

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). https://doi.org/10.1007/s00013-015-0736-7

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  • DOI: https://doi.org/10.1007/s00013-015-0736-7

Mathematics Subject Classification

  • 47A16
  • 30A76
  • 30H10

Keywords

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