Acknowledgement
We are very grateful to the referees for their careful reading, suggestions and corrections which improved the quality of our paper.
References
- M. Ansari, Strong topological transitivity of some classes of operators, Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 677-685. https://projecteuclid.org/euclid.bbms/1547780428 https://doi.org/10.36045/bbms/1547780428
- S. I. Ansari, Hypercyclic and cyclic vectors, J. Funct. Anal. 128 (1995), no. 2, 374-383. https://doi.org/10.1006/jfan.1995.1036
- M. Ansari, B. Khani-Robati, and K. Hedayatian, On the density and transitivity of sets of operators, Turkish J. Math. 42 (2018), no. 1, 181-189. https://doi.org/10.3906/mat-1508-87
- F. Bayart and E. Matheron, Dynamics of linear operators, Cambridge Tracts in Mathematics, 179, Cambridge University Press, Cambridge, 2009. https://doi.org/10.1017/CBO9780511581113
- J. Bes and A. Peris, Hereditarily hypercyclic operators, J. Funct. Anal. 167 (1999), no. 1, 94-112. https://doi.org/10.1006/jfan.1999.3437
- G. D. Birkhoff, Surface transformations and their dynamical applications, Acta Math. 43 (1922), no. 1, 1-119. https://doi.org/10.1007/BF02401754
- P. S. Bourdon, Invertible weighted composition operators, Proc. Amer. Math. Soc. 142 (2014), no. 1, 289-299. https://doi.org/10.1090/S0002-9939-2013-11804-6
- G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal. 98 (1991), no. 2, 229-269. https://doi.org/10.1016/0022-1236(91)90078-J
- K.-G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Universitext, Springer, London, 2011. https://doi.org/10.1007/978-1-4471-2170-1
- A. Kameyama, Topological transitivity and strong transitivity, Acta Math. Univ. Comenian. (N.S.) 71 (2002), no. 2, 139-145.
- C. Kitai, Invariant closed sets for linear opeartors, ProQuest LLC, Ann Arbor, MI, 1982.
- F. Leon-Saavedra and V. Muller, Rotations of hypercyclic and supercyclic operators, Integral Equations Operator Theory 50 (2004), no. 3, 385-391. https://doi.org/10.1007/s00020-003-1299-8
- V. Muller and J. Vrsovsky, Orbits of linear operators tending to infinity, Rocky Mountain J. Math. 39 (2009), no. 1, 219-230. https://doi.org/10.1216/RMJ-2009-39-1-219
- C. J. Read, The invariant subspace problem for a class of Banach spaces. II. Hypercyclic operators, Israel J. Math. 63 (1988), no. 1, 1-40. https://doi.org/10.1007/BF02765019
- W. Rudin, Real and Complex Analysis, third edition, McGraw-Hill Book Co., New York, 1987.
- H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993-1004. https://doi.org/10.2307/2154883