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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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