Quasi-Mixing C₀-Semigroups and Their Relations With Recurrent C₀-Semigroups

Authors

• Mansooreh Moosapoor, Associate Professor, Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, IranFollow
• Otmane Benchiheb, Department of Mathematics, Chouaib Doukkali University, Faculty of Science, P.O. Box 20. 24000, El Jadida, MoroccoFollow

Abstract

This article presents and investigates the concept of the quasi-mixing C₀-semigroups. It is proved that the quasi-mixing of an invertible C₀-semigroup is equivalent to the quasi-mixing of its inverse. The quasi-mixing vectors are defined and they are used to prove a sufficient condition for the quasi-mixing. It is established that the quasi-mixing of a C₀-semigroup is equivalent to the quasi-mixing of any of its discretizations. The quasi-mixing of a C₀-semigroup ( T_t )_{t ≥ 0}, as it is demonstrated by this study, implies the quasi-mixing for each operator T_t, t ≥ 0. It is proved that the quasi-mixing of the direct sum of two C₀-semigroups is equivalent to the quasi-mixing of both semigroups. Furthermore, some relations between the quasi-mixing and the recurrence are explored in this article. It is shown that the operators of a quasi-mixing C₀-semigroup are recurrent. Also, it is demonstrated that the recurrence of every discretization of a C₀-semigroup is equivalent to the quasi-mixing of the C₀-semigroup.

Keywords

Direct sum, Mixing, Quasi-mixing semigroups, Recurrent semigroups, Semigroups

Subject Area

Mathematics

Article Type

Article

First Page

2188

Last Page

2194

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Moosapoor, Mansooreh and Benchiheb, Otmane (2026) "Quasi-Mixing C₀-Semigroups and Their Relations With Recurrent C₀-Semigroups," Baghdad Science Journal: Vol. 23: Iss. 6, Article 18.
DOI: https://doi.org/10.21123/2411-7986.5332