Cesàro hypercyclicity and transitivity for $C_0$-semigroups
نویسندگان
1 Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.
2 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
doi
10.30504/jims.2026.559943.1298چکیده
In this paper, we introduce the concepts of Cesàro hypercyclicity and Cesàro transitivity for $C_0$-semigroups. We prove that a $C_0$-semigroup is Cesàro transitive if and only if it possesses a dense set of Cesàro hypercyclic vectors. Subsequently, we demonstrate that Cesàro transitive $C_0$-semigroups are hypercyclic. Also, we provide an example of a Cesàro hypercyclic $C_0$-semigroup that is not hypercyclic. We establish that if a $C_0$-semigroup contains a Cesàro hypercyclic operator, then the entire semigroup is Cesàro hypercyclic. Furthermore, we characterize the structure of Cesàro hypercyclic vectors. Additionally, we define sequentially Cesàro mixing $C_0$-semigroups that is a subset of Cesàro hypercyclic $C_0$-semigroups. We provide certain criteria for sequential Cesàro mixing, and use them to make an example of a Cesàro mixing $C_0$-semigroup.
