7 papers
Hypercyclic shifts on lattice graphs
Anton Baranov, Andrei Lishanskii, Dimitris Papathanasiou
Recently K.-G. Grosse-Erdmann and D. Papathanasiou described hypercyclic shifts in weighted spaces on directed trees. In this note we discuss several simple examples of graphs whic…
Point spectrum and hypercyclicity problem for a class of truncated Toeplitz operators
Anton Baranov, Andrei Lishanskii
In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of trunc…
New classes of hypercyclic Toeplitz operators
Evgeny Abakumov, Anton Baranov, Stéphane Charpentier +1
We study hypercyclicity of Toeplitz operators in the Hardy space with symbols of the form , where is a rational function and $ϕ\in H^\i…
On hypercyclic rank one perturbations of unitary operators
Anton Baranov, Vladimir Kapustin, Andrei Lishanskii
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…
Hypercyclic Toeplitz operators
Anton Baranov, Andrei Lishanskii
We study hypercyclicity of the Toeplitz operators in the Hardy space with symbols of the form , where is a polynomial and $ϕ\in H^\infty(\ma…
On S. Grivaux' example of a hypercyclic rank one perturbation of a unitary operator
Anton Baranov, Andrei Lishanskii
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 func…
A class of Toeplitz operators with hypercyclic subspaces
Andrei Lishanskii
We use a theorem by Gonzalez, Leon-Saavedra and Montes-Rodriguez to construct a class of coanalytic Toeplitz operators which have an infinite-dimensional closed subspace, where any…