Turkish Journal of Mathematics
Article Title
DOI
10.3906/mat-1512-40
Abstract
In this note, we study topologically transitive and hypercyclic composition operators on $C_p(X)$ or $C_k(X)$. We prove that if $G$ is a semigroup of continuous self maps of a countable metric space $X$ with the following properties: (1) every element of $G$ is one-to-one on $X$, (2) the action of $G$ is strongly run-away on $X$, then the action of $\hat{G}$ on $C_p(X)$ is topologically transitive and hypercyclic. If $G$ is the set of all one-to-one and continuous self maps of $\mathbb{R}\setminus \mathbb{Z}$, then the action of $\hat{G}$ on $C_k(\mathbb{R}\setminus \mathbb{Z})$ is hypercyclic. We also show that the action of $\hat{G}$ on $C_p(\omega_1)$ is not hypercyclic.
First Page
186
Last Page
192
Recommended Citation
PENG, LIANGXUE and YANG, CHONG
(2017)
"A note on dynamics in functional spaces,"
Turkish Journal of Mathematics: Vol. 41:
No.
1, Article 17.
https://doi.org/10.3906/mat-1512-40
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss1/17
