Hypercyclicity of weighted translations on locally compact Hausdorff spaces. Issue 3 (3rd July 2021)

• Record Type: Journal Article
• Authors: Wang, Ya; Zhou, Ze-Hua
• Is Part Of: Dynamical systems. Volume 36:Issue 3(2021)
• Page Start: 507
• Page End: 526
• Publication Date: 2021-07-03
• Subjects: Hypercyclicity -- weighted translation -- locally compact Hausdorff space; 47A16 -- 47B38 -- 46E15; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2021.1931814
• Languages: English
• ISSNs: 1468-9367

Abstract

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.