On the existence of subspace-diskcyclic $C_{0}$-semigroups and some criteria

Document Type : Research Paper

Author

Department of Mathematics, Farhangian University, Tehran, Iran.

Abstract

In this paper,  we prove the existance of subspace-diskcyclic $C_{0}$-semigroups   on any infinite-dimensional   separable Banach space.  We state that diskcyclic $C_{0}$-semigroups are subspace-diskcyclic. Also, we establish some criteria for subspace-diskcyclic $C_{0}$-semigroups. Most of these criteria  are based on non-empty relatively open sets  and some of them are based on dense sets.

Keywords

References

[1] M.R. Azimi, Subspace-diskcyclic sequences of linear operators, Sahand Communications in Mathematical Analysis vol.8, no.1 (2017) 97{106.
[2] N. Bamerni, A. Kilicman, On Subspace-diskcyclicity, Arab Journal of Mathematical Sciences vol.23, no.2 (2017) 133{140.
[3] N. Bamerni, A. Kilicman, and M. S. Md. Noorani, A review of some works in the theory of diskcyclic operators, Bulletin of the Malaysian Mathematical Sciences Society vol.39, no.2 (2016) 723{739.
[4] N. Bamerni, V. Kadets, and A. Kilicman, Hypercyclic operators are subspace hypercyclic, Journal of Mathematical Analysis and Applications vol.435, no.2 (2016) 1812{1815.
[5] N. Bamerni, A. Kilicman, Operators with diskcyclic vectors subspaces, Journal of Taibah University for Science vol.9, no.3 (2015) 414{419.
[6] L. Bernal-Gonzalez and K.G. Grosse-Erdmann, Existence and Nonexistence of Hypercyclic Semigroups, Proceedings of the American Mathematical Society vol.135 (2007) 755{766.
[7] J. A. Conejero, V. Muller, A. Peris, Hypercyclic behaviour of operators in a hypercyclic C0-semigroup, Journal of functional analysis vol.244 (2007) 342{348.
[8] J. A. Conejero, A. Peris, Linear transitivity, Topology and Its Applications vol.153 (2005) 767{773.
[9] W. Desh, W. Schappacher, and G.F.Webb, Hypercyclic and chaotic semigroups of linear operators, Ergodic Theory and Dynamical Systems vol.17 (1997) 793{819.
[10] C. T. J. Dodson, A review of some recent work on hypercyclicity, Balkan Journal of Geometry and Its Applications vol.19, no.1 (2014) 22{41.
[11] K.G. Grosse-Erdmann and A. Peris Manguillot, Linear chaos, Springer, London, 2011.
[12] M. Moosapoor, Diskcyclic C0-semigroups and diskcyclicity criteria, Nonlinear Functional Analysis and Applications vol.27, no.1 (2022) 111{119.
[13] M. Moosapoor, Some criteria for subspace-hypercyclicity of C0-semigroups, Australian journal of mathematical analysis and applications vol.18, no.1 (2021) Art. 12, 8 pp.
[14] A. Tajmouati, A. El Bakkali, and A. Toukmati, On some properties of M-hypercyclic C0-semigroup, Italian journal of pure and applied mathematics vol.35 (2015) 351{360.
[15] Z. J. Zeana, Cyclic phenomena of operators on Hilbert space, Thesis, University of Baghdad, 2002.

Files

History

  • Receive Date: 22 September 2022
  • Revise Date: 16 December 2022
  • Accept Date: 19 February 2023

Share

How to cite

Statistics