广东工业大学学报 ›› 2021, Vol. 38 ›› Issue (03): 62-64.doi: 10.12052/gdutxb.200092

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加权复合算子从Bloch型空间到圆盘代数的拓扑结构

许丽葵, 邓秀勤, 刘军明   

  1. 广东工业大学 应用数学学院，广东 广州 510520
  • 收稿日期:2020-07-22 出版日期:2021-05-10 发布日期:2021-03-12
  • 通信作者: 刘军明 (1985-)，男，讲师，主要研究方向为函数空间，E-mail：jmliu@gdut.edu.cn E-mail:jmliu@gdut.edu.cn
  • 作者简介:许丽葵 (1994-)，女，硕士研究生，主要研究方向为函数空间
  • 基金资助:
    国家自然科学基金资助项目(11801094)

The Topological Structure of Weighted Composition Operators from Bloch Type Spaces to the Disk Algebra

Xu Li-kui, Deng Xiu-qin, Liu Jun-ming   

  1. School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2020-07-22 Online:2021-05-10 Published:2021-03-12

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摘要： 设$ A$为圆盘代数, $ u$和$ \varphi $是$ A$上的解析函数, 刻画了加权复合算子$ u{C_\varphi }$从Bloch型空间到圆盘代数的一些范数估计。同时还研究了加权复合算子空间的道路连通性, 得知任意2个有界加权复合算子是道路连通的。

关键词: 拓扑结构, 加权复合算子, Bloch型空间, 圆盘代数, 道路连通性

Abstract: Let $ A$ be the disk algebra, $ u$ and $ \varphi $ be analytic functins on A, some estimates of weighted composition operators $ u{C_\varphi }$ from Bloch type spaces to the disk algebra are characterized. At the same time, the path connectedness of the space of weighted composition operators is investigated and a conclusion is derived that any two bounded weighted composition operators are pathwise connected.

Key words: topological structure, weighted composition operators, Bloch type spaces, disk algebra, path connectedness

中图分类号: 

  • O174.5
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