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# Disjoint Hypercyclicity and Weighted Translations on Discrete Groups

Published:2016-12-09
Printed: Dec 2017
• Chung-Chuan Chen,
Department of Mathematics Education, National Taichung University of Education, Taiwan
 Format: LaTeX MathJax PDF

## Abstract

Let $1\leq p\lt \infty$, and let $G$ be a discrete group. We give a sufficient and necessary condition for weighted translation operators on the Lebesgue space $\ell^p(G)$ to be densely disjoint hypercyclic. The characterization for the dual of a weighted translation to be densely disjoint hypercyclic is also obtained.
 Keywords: disjoint hypercyclicity, topological transitivity, weighted translation, $\ell^p$-space
 MSC Classifications: 47A16 - Cyclic vectors, hypercyclic and chaotic operators 47B38 - Operators on function spaces (general) 43A15 - $L^p$-spaces and other function spaces on groups, semigroups, etc.

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