厦门大学学报（自然科学版）2025，Vol.64Issue(6)：1022-1025,4.DOI:10.6043/j.issn.0438-0479.202411022
连续函数空间上复合算子的拓扑传递性质
Topologically transitive properties of composition operators on continuous function spaces
陆毅 1杨冲 1孙英华2
作者信息
- 1. 华北电力大学河北省物理学与能源技术重点实验室,数理学院,河北 保定 071003
- 2. 厦门大学数学科学学院,福建 厦门 361005
- 折叠
摘要
Abstract
[Objective]The study of the topological transitivity and disjoint topological transitivity of the composition operator Cφand the weighted composition operator Cω,φ on the continuous function space C(Ω)endowed with a compact-open topology on the simple connected domain Ω on the complex plane C has attracted considerable research attention.Herein we participate in this study.[Methods]Based on definitions of composition operators,weighted composition operators,topological transitivity,and disjoint topological transitivity,a new lemma is derived through algebraic properties,and Tietze's extension theorem.Next,compact-open topological properties are comprehensively applied to study the problem.[Results]An equivalent characterization of the topologically transitive composition operator Cr on the continuous function space is given.Furthermore,a sufficient condition for the topologically transitive weighted composition operator Cω,φ,an equivalent characterization of the disjoint topologically transitive composition operator Cφ,and a sufficient condition for the disjoint topologically transitive weighted composite operator Cω,φ are also given.[Conclusions]The proposed study characterizes the topologically transitive and disjoint topologically transitive(weighted)composition operators on continuous function spaces.It may serve as a guiding reference for the research of composite operators on the continuous function space and effectively promotes the development of related fields.关键词
复合算子/拓扑传递/不交拓扑传递Key words
composition operator/topological transitivity/disjoint topological transitivity分类
数理科学引用本文复制引用
陆毅,杨冲,孙英华..连续函数空间上复合算子的拓扑传递性质[J].厦门大学学报（自然科学版）,2025,64(6):1022-1025,4.
