2017/11/26 by Baranov, Anton, Kapustin, Vladimir, Lishanskii, Andrei
#FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1711.09479
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.