Hypercyclicity of weighted translations on locally compact Hausdorff spaces. Issue 3 (3rd July 2021) - Wang, Ya; Zhou, Ze-Hua
Abstract : Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure and ω is a weight on G . In this article, we provide necessary and sufficient conditions for the hypercyclic weighted translations acting on the weighted space L p ( G, ω ) ( 1 ≤ p < ∞ )   in two different cases. Also, some examples are given to illustrate that the results in the first case generalize the characterizations on hypercyclicity for unilateral weighted shifts studied by Salas [16], and the results in the second case generalize Chen and Chu's work in [8]. Furthermore, we give characterizations of hypercyclicity for adjoint operators of these weighted translations.