Disjoint Hypercyclicity and Weighted Translations on Discrete Groups

Abstract

Let 1 ≤ p < ∞, and let G be a discrete group. We give a sufficient and necessary condition for weighted translation operators on the Lebesgue space ℓp(G) to be densely disjoint hypercyclic. The characterization for the dual of a weighted translation to be densely disjoint hypercyclic is also obtained.