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arXiv · 1711.09479

On hypercyclic rank one perturbations of unitary operators

Anton Baranov·Vladimir Kapustin·Andrei Lishanskii
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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 Carleson set on the circle can be the spectrum of a perturbed (hypercyclic) operator.

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Anton Baranov, Vladimir Kapustin, Andrei Lishanskii. 2017-11-26. On hypercyclic rank one perturbations of unitary operators. https://arxiv.org/abs/1711.09479

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