Document Type : Research Paper


1 Associate Professor, Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.

2 Associate Professor, Department of Mathematics, Payame Noor University, Tehran, Iran.


In this article, we introduce quasi-mixing operators and construct various examples. We prove that quasi-mixing operators exist on all finite-dimensional and infinite-dimensional  Banach spaces. We also prove that an invertible operator $T$ is quasi-mixing if and only if $T^{-1}$ is quasi-mixing. We state some sufficient conditions  under which an operator is quasi-mixing. Moreover, we prove that the direct sum of two operators is quasi-mixing if and only if any of them is quasi-mixing.


Main Subjects

1. M. Ansari, Supermixing and hypermixing operators, J. Math. Anal. Appl., 498 (2021), Article ID 124952, 14p.
2. F. Bayart, U. B. Darji and B. Pires, Topological transitivity and mixing of composition operators, J. Math. Anal. Appl., 465(1) (2018), pp. 125-139.
3. J. Bes, A. Peris and Y. Puig, Strong transitivity properties for operators, J. Differ. Equ., 266 (2-3) (2019), pp. 1313-1337.
4. J. Bes and A. Peris, Hereditarily hypercyclic operators, J. Func. Anal., 167 (1999), pp. 94-112.
5. G. Costakis and M. Sambarino, Topologically mixing hypercyclic operators, Proc. Amer. Math. Soc., 132 (2004), pp. 385-389.
6. C.T.J. Dodson, A review of some recent work on hypercyclicity, Balk. J. Geo. App., 19 (2014), pp. 22-41.
7. K.G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Springer-Verlag, London, 2011.
8. S. Grivaux, Hypercyclic operators, mixing operators, and the bounded steps problem, J. Operator Theory, 54 (1) (2005), pp. 147-168.
9. M. Moosapoor, Supermixing and hypermixing of strongly continuous semigroups and their direct sum, J. Taibah Univ. Sci., 15 (1) (2021), pp. 953-959.
10. M. Moosapoor and M. Shahriari, About Subspace-frequently Hypercyclic Operators, Sahand Commun. Math. Anal., 17 (3) (2020), pp. 107-116.
11. Z. Rong, Hypercyclic and mixing composition operators on Hp, arXiv preprint, arXiv:2207.05274(2022).