IJPAM: Volume 117, No. 1 (2017)

Title

HYPERCYCLIC WEIGHTS ON HYPERGROUPS

Authors

Chung-Chuan Chen$^1$, Seyyed Mohammad Tabatabaie$^2$
$^1$Department of Mathematics Education
National Taichung University of Education
Taichung 403, TAIWAN
$^2$Department of Mathematics
University of Qom
Qom, IRAN

Abstract

Let $K$ be a locally compact hypergroup and $1\leq p < \infty$. In this paper, we study sequences of operators, generated by a weight and a sequence of elements of $K$, on the Lebesgue space $L^p(K)$. A weight is called hypercyclic if its related sequence of operators is hypercyclic. Some sufficient and necessary conditions for a weight to be hypercyclic are obtained. By focusing on the elements of center of $K$, we refine the results and give the characterization for such a weight to be hypercyclic. Hypercyclicity on strong hypergroups is investigated as well.

History

Received: 2017-08-21
Revised: 2017-09-12
Published: November 29, 2017

AMS Classification, Key Words

AMS Subject Classification: 43A62, 47A16, 43A15
Key Words and Phrases: locally compact hypergroup, hypercyclicity, topological transitivity, chaos, $L^p$-space

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How to Cite?

DOI: 10.12732/ijpam.v117i1.12 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 117
Issue: 1
Pages: 125 - 142


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