Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

Cesàro hypercyclicity and transitivity for $C_0$-semigroups

Document Type : Research Article

Authors
M. Moosapoor 1
M. Shams Yousefi 2
1 Department of Mathematics Education, Farhangian University, P.O. Box 14665-889, Tehran, Iran.
2 Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
10.30504/jims.2026.559943.1298
Abstract
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.
Keywords
Cesà
ro hypercyclicity
sequentially Cesà
ro mixing
semigroups
criteria
Subjects
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Journal of the Iranian Mathematical Society
Volume 7, Issue 1
This issue is in progress but all papers are fully citable
February 2026
Pages 35-42