On hypercyclic rank one perturbations of unitary operators
Functional Analysis
2017-11-28 v1
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.
Keywords
Cite
@article{arxiv.1711.09479,
title = {On hypercyclic rank one perturbations of unitary operators},
author = {Anton Baranov and Vladimir Kapustin and Andrei Lishanskii},
journal= {arXiv preprint arXiv:1711.09479},
year = {2017}
}