Archiv der Mathematik

, Volume 104, Issue 3, pp 223–235

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


DOI: 10.1007/s00013-015-0736-7

Cite this article as:
Baranov, A. & Lishanskii, A. Arch. Math. (2015) 104: 223. doi:10.1007/s00013-015-0736-7


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.


Hypercyclic operator Rank one perturbation Inner function Model space Functional model 

Mathematics Subject Classification

47A16 30A76 30H10 

Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsSt. Petersburg State UniversitySt. PetersburgRussia
  2. 2.National Research University Higher School of EconomicsSt. PetersburgRussia
  3. 3.Chebyshev LaboratorySt. Petersburg State UniversitySt. PetersburgRussia

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