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On hypercyclic rank one perturbations of unitary operators

Author

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  • Anton Baranov
  • Vladimir Kapustin
  • Andrei Lishanskii

Abstract

Recently, S. Grivaux showed that there exists a rank one perturbation of a unitary operator in a Hilbert space which is hypercyclic. Another construction was suggested later by the first and the third authors. Here, using a functional model for rank one perturbations of singular unitary operators, we give yet another construction of hypercyclic rank one perturbation of a unitary operator. In particular, we show that any countable union of perfect Carleson sets on the circle can be the spectrum of a perturbed (hypercyclic) operator.

Suggested Citation

  • Anton Baranov & Vladimir Kapustin & Andrei Lishanskii, 2019. "On hypercyclic rank one perturbations of unitary operators," Mathematische Nachrichten, Wiley Blackwell, vol. 292(5), pages 961-968, May.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:5:p:961-968
    DOI: 10.1002/mana.201800242
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