On Cesaro-Hypercyclic Operators

El Berrag, Mohammed

doi:10.28924/2291-8639-22-2024-49

Research Article

On Cesaro-Hypercyclic Operators

Mohammed El Berrag

Abstract

In this paper we characterize some properties of the Cesaro-Hypercyclic and mixing operators. At the same time, we also give a Cesaro-Hypercyclicity criterion and offer an example of this criterion.

How to Cite

M. El Berrag, On Cesaro-Hypercyclic Operators, Int. J. Anal. Appl. 22 (2024), 49. https://doi.org/10.28924/2291-8639-22-2024-49

BibTeX

@article{Berrag2024,
  author  = {El Berrag, Mohammed},
  title   = {On Cesaro-Hypercyclic Operators},
  journal = {Int. J. Anal. Appl.},
  volume  = {22},
  year    = {2024},
  pages   = {49},
  doi     = {10.28924/2291-8639-22-2024-49}
}

References

[1] F. Bayart, E. Matheron, Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009.
[2] T. Bermúdez, A. Bonilla and A. Peris, On Hypercyclicity and Supercyclicity Criteria, Bull. Aust. Math. Soc. 70 (2004), 45–54. https://doi.org/10.1017/s0004972700035802.
[3] P.S. Bourdon, J.H. Shapiro, Cyclic Phenomena for Composition Operators, American Mathematical Society, Providence, 1997.
[4] M. El Berrag, A. Tajmouati, ON SUBSPACE-SUPERCYCLIC SEMIGROUP, Commun. Korean Math. Soc. 33 (2018), 157–164. https://doi.org/10.4134/CKMS.C170047.
[5] N. Feldman, Hypercyclicity and Supercyclicity for Invertible Bilateral Weighted Shifts, Proc. Amer. Math. Soc. 131 (2003), 479-485.
[6] N. Feldman, V. Miller, L. Miller, Hypercyclic and Supercyclic Cohyponormal Operators, Acta Sci. Math. 68 (2002), 303–328.
[7] R.M. Gethner, J.H. Shapiro, Universal Vectors for Operators on Spaces of Holomorphic Functions, Proc. Amer. Math. Soc. 100 (1987), 281–288.
[8] C. Kitai, Invariant Closed Sets for Linear Operators, Dissertation, University of Toronto, 1982.
[9] K.G. Grosse-Erdmann, A.P. Manguillot, Linear Chaos, Springer, London, 2011.
[10] H.M. Hilden, L.J. Wallen, Some Cyclic and Non-Cyclic Vectors of Certain Operator, Indiana Univ. Math. J. 23 (1974), 557–565. https://www.jstor.org/stable/24890788.
[11] F. León-Saavedra, Operators With Hypercyclic Cesàro Means, Stud. Math. 152 (2002), 201–215.
[12] S. Rolewicz, On Orbits of Elements, Stud. Math. 32 (1969), 17–22.
[13] H.N. Salas, Hypercyclic Weighted Shifts, Trans. Amer. Math. Soc. 347 (1995), 993–1004.
[14] H.N. Salas, Supercyclicity and Weighted Shifts, Stud. Math. 135 (1999), 55–74.
[15] A. Tajmouati, M. El Berrag, Some Results on Hypercyclicity of Tuple of Operators, Italian J. Pure Appl. Math. 35 (2015), 487–492.