International Journal of Nonlinear Analysis and Applications

Weakly disk-cyclic mixing operators

Document Type : Research Paper

Authors

1 Department of Mathematics, College of Education for Pure Science (Ibn Al Haitham), Baghdad University, Iraq

2 Department of Mathematics, College of Science, Baghdad University, Iraq

Abstract

It is known that there are disk-cyclic operators that are not satisfy the disk-cyclic criterion. This work introduce weakly disk-cyclic operators, which are kind of disk-cyclic operators, and study its relation with disk-cyclic criterion with several results and properties.

Keywords

[1] N. Bamerni, Cyclicity of bunded linear operators on suparable banach spaces and closed subspaces, Ph.D. Thesis,
University Putra Malaysia, 2016.
[2] F. Bayart and E. Matheron, Dynamics of linear operators, Cambridge university press, France, 2009.
[3] B. Beauzamy,Introdction to operator theory and invariant subspaces, Elsevier Science Publishers B. V., 1988.
[4] G. Godefroy and J. H. Shapiro, Operator with dense, invariant cyclic vector manifolds, J. Functional analysis,
2 (1991) 229-269.
[5] H. M. Hilden and L. J. Wallen,Some cyclic and non-cyclic vectors of certain operator, Indiana Univ. Math. J.,
23 (1974) 557-565.
[6] Z. Jamil, Cyclic phenomena of operators on Hilbert space, Ph.D. Thesis, University of Baghdad, 2002.
[7] C. Kitai,Invariant closed sets for linear operators, Ph.D. Thesis, University of Toronto, 1982.
[8] Y. Liang and Z. Zhou, Disk-cyclic and codisk-cyclic tuples of the adjoint weighted composition operators on Hilbert
spaces, Bulletin of the Belgian Mathematical Society - Simon Stevin, 23 (2016) 203–215.
[9] F. L. Saavedra and V. Müller, Rotations of hypercyclic and supercyclic operators, Integr. equ. oper. theory, 50
(2004) 385–391.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 2531-2537
  • Receive Date: 28 March 2021
  • Accept Date: 16 May 2021