Hypercyclicity of weighted translations on locally compact Hausdorff spaces
Hypercyclicity of weighted translations on locally compact Hausdorff spaces
复制标题
局部紧豪斯多夫空间上加权平移的超循环性
DOI：
10.1080/14689367.2021.1931814
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Zhou Ze-Hua
中科院分区：
文献类型：
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作者：
Wang Ya;Zhou Ze-Hua
设G是一个局部紧的第二可数Hausdorff空间，具有正的正则Borel测度，ω是G上的一个权.本文在两种不同的情形下给出了加权空间上超循环加权平移的充要条件，并举例说明第一种情形的结果推广了Salas [16]关于单侧加权移位的超循环性的刻画，第二种情形的结果推广了Chen和Chu [8]的结果.此外，我们给出了这些加权平移的伴随算子的超循环性的刻画。
LetGbe a locally compact second countable Hausdorff space with a positive regular Borel measure and ω is a weight onG. In this article, we provide necessary and sufficient conditions for the hypercyclic weighted translations acting on the weighted spacein 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.