Mathematical  Culture and Thought

Mathematical Culture and Thought

Disk-recurrent Operators and Their Properties

Document Type : Original

Author
Department of Mathematics, Farhangian University, Iran
Abstract
In this article, the new concept of disk-recurrent operators is introduced.
We prove that an operator is disk-recurrent if and only if it has a dense set of diskrecurrent
vectors. We prove that these operators can be found in infinite dimensional
and also finite dimensional Banach spaces. In addition, we show that the operator T
is disk-recurrent if and only if Tn is disk-recurrent. We also observe that if the diskrecurrence
of the direct sum of two operators is disk-recurrent, then any of them is
disk-recurrent and we express some results about this.
Keywords

Subjects


[1]Amouch, M., Benchiheb, O., On super-recurrent operators (2021).
[2]Bes, J., Peris, A., Hereditarily hypercyclic operators, J. Funct. Anal., 167 (1999), 94-112.
[3]Costakis, G., Manoussos, A., Parissis, I., Recurrent linear operators, Complex Anal. Oper. Theory,
8 (2014), 1601-1643.
[4]Dodson, C. T. J., A review of some recent work on hypercyclicity, Balkan J. Geom. Appl., 19 (2014),
22-41.
[5]Furstenberg, H., Recurrence in Ergodic Theory and Combinatorialn Number Theory, Princeton University
Press, NJ, 1981.
[6]Gottschalk, W. H., Hedlund, G. H., Topological Dynamics, American Mathematical Society, Rhode
Island, Providence, 1994.
[7]Grosse-Erdmann, K. G., Peris Manguillot, A., Linear Chaos, Springer-Verlag, London, 2011.
[8]Grosse-Erdmann, K. G., Recent developments in hypercyclicity, Rev. R. Acad. Cienc. Exactas Fis.
Nat., 97 (2003), 273-286.
[9]Grosse-Erdmann, K. G., Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.),
36 (1999), 345-381.
[10]Moosapoor, M., On subspace-recurrent operators, Tamkang J. Math., 53 (2022), 363-371.
[11]Moosapoor, M., On the recurrentC0-semigroups, their existence and some criteria, J. Math., (2021),
Article ID 6756908.
Volume 41, Issue 2 - Serial Number 71
December 2022
Pages 119-128

  • Receive Date 03 February 2022
  • Revise Date 25 September 2022
  • Accept Date 25 September 2022
  • Publish Date 21 January 2023