Czechoslovak Mathematical Journal, Vol. 67, No. 3, pp. 839-853, 2017


Disjoint hypercyclic powers of weighted translations on groups

Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, Ze-Hua Zhou

Received April 27, 2016.   First published August 10, 2017

Abstract:  Let $G$ be a locally compact group and let $1 \le p < \infty.$ Recently, Chen et al. characterized hypercyclic, supercyclic and chaotic weighted translations on locally compact groups and their homogeneous spaces. There has been an increasing interest in studying the disjoint hypercyclicity acting on various spaces of holomorphic functions. In this note, we will study disjoint hypercyclic and disjoint supercyclic powers of weighted translation operators on the Lebesgue space $L^p(G)$ in terms of the weights. Sufficient and necessary conditions for disjoint hypercyclic and disjoint supercyclic powers of weighted translations generated by aperiodic elements on groups will be given.
Keywords:  disjoint hypercyclic powers of weighted translations; aperiodic element; locally compact group
Classification MSC:  47A16, 47B38, 46E15
DOI:  10.21136/CMJ.2017.0204-16


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Affiliations:   Liang Zhang, Hui-Qiang Lu, Xiao-Mei Fu, School of Marine Science and Technology, Tianjin University, 92 Weijin Road, 300072 Tianjin, Nankai, P. R. China, e-mail: 168zhangliang2011@163.com, liangzhang@tju.edu.cn, chentu90@163.com, fuxiaomei@tju.edu.cn; Ze-Hua Zhou (corresponding author), Department of Mathematics, Tianjin University, 92 Weijin Road, 300072 Tianjin, Nankai, P. R. China, e-mail: zehuazhoumath@aliyun.com, zhzhou@tju.edu.cn

 
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