References
- Ansari S.I. Existence of hypercyclic operators on topological
vector spaces. J. Funct. Anal. 1997, 148 (2),
384–390. doi:10.1006/JFAN.1996.3093
- Aron R.M., Bès J. Hypercyclic differentiation operators.
Contemporary Math. 1999, 232, 39–46.
doi:10.1090/conm/232/03382
- Bayart F., Matheron E. Dynamics of linear operators. In: Bertoin J.
(Ed.) Cambridge Tracts in Mathematics, 179. Cambridge University Press,
New York, 2009.
- Bermúdez T., Kalton N.J. The range of operators on von Neumann
algebras. Proc. Amer. Math. Soc. 2002, 130 (5),
1447–1455.
- Bernal-González L. On hypercyclic operators on Banach
spaces. Proc. Amer. Math. Soc. 1999, 127,
1003–1010. doi:10.1090/S0002-9939-99-04657-2
- Bes J., Chan K.C., Sanders R. Weak-Star Hypercyclicity and
Supercyclicity of Shifts on \(l^\infty\). Integral Equations
Operator Theory 2006, 55, 363–376.
- Birkhoff G.D. Démonstration d'un théorème élémentaire sur les
fonctions entières. Gauthier-Villars, Paris 1929.
- Bourdon P.S., Shapiro J.H. Cyclic phenomena for composition
operators. Mem. Amer. Math. Soc. 1997, 125 (596),
1–46. doi:10.1090/memo/0596
- Chan K.C., Shapiro J.H. The cyclic behavior of translation
operators on Hilbert spaces of entire functions. Indiana Univ.
Math. J. 1991, 40, 1421–1449.
- Chan K.C. Hypercyclicity of the operator algebra for a separable
Hilbert space. J. Operator Theory 1999, 42,
231–244.
- Chernega I., Holubchak O., Novosad Z., Zagorodnyuk A. Continuity
and hypercyclicity of composition operators on algebras of symmetric
analytic functions on Banach spaces. Eur. J. Math. 2020,
6, 153–163. doi:10.1007/s40879-019-00390-z
- Devaney L.R. An introduction to chaotic dynamical systems.
Addison-Wesley, Reedwood City, 1989.
- Godefroy G., Shapiro H.J. Operators with dense, invariant, cyclic
vector manifolds. J. Funct. Anal. 1991, 98 (2),
229–269. doi:10.1016/0022-1236(91)90078-J
- Lopushansky O., Zagorodnyuk A. Hardy type spaces associated with
compact unitary groups. Nonlinear Anal. 2011, 74
(2), 556–572. doi:10.1016/j.na.2010.09.009
- Lopushansky O., Zagorodnyuk A. Representing measures and
infinite-dimensional holomorphy. J. Math. Anal. Appl. 2007,
333 (2), 614–625.
- Manoussos A. A Birkhoff type transitivity theorem for
non-separable completely metrizable spaces with applications to linear
dynamics. J. Operator Theory 2013, 70 (1),
165–174. doi:10.7900/jot.2011may12.1971
- Montes-Rodríguez A., Romero-Moreno C. Supercyclicity in the
operator algebra. Studia Math. 2002, 150, 201–213.
doi:10.4064/sm150-3-1
- Mozhyrovska Z.H., Zagorodnyuk A.V. Hypercyclic behavior of
translation operators on spaces of analytic functions on Hilbert
spaces. J. Funct. Spaces 2015, 2015, article ID
139289. doi:10.1155/2015/139289
- Novosad Z., Zagorodnyuk A. Analytic Automorphisms and
Transitivity of Analytic Mappings. Mathematics 2020,
8 (12), 2179. doi:10.3390/math8122179
- Novosad Z., Zagorodnyuk A. Polynomial automorphisms and
hypercyclic operators on spaces of analytic functions. Arch. Math.
2007, 89, 157–166. doi:10.1007/s00013-007-2043-4
- Rolewicz S. On orbits of elements. Studia Math. 1969,
32 (1), 17–22.
- Zagorodnyuk A., Novosad Z. Topological Transitivity of Shift
Similar Operators on Nonseparable Hilbert Spaces. J. Funct. Spaces
2021, 2021, article ID 9306342.
doi:10.1155/2021/9306342