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

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

doi:10.12052/gdutxb.200092

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

更新时间：2026-05-27

- The Topological Structure of Weighted Composition Operators from Bloch Type Spaces to the Disk Algebra
- Vol. 38, Issue 3, Pages: 62-64(2021)
- 作者机构：
  
  广东工业大学应用数学学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.200092
  CLC： O174.5
- Online First：10 May 2021，
  
  Published：2021
- 稿件说明：
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许丽葵, 邓秀勤, 刘军明. 加权复合算子从Bloch型空间到圆盘代数的拓扑结构[J]. 广东工业大学学报, 2021, 38(3): 62-64.

Xu Li-kui, Deng Xiu-qin, Liu Jun-ming. The Topological Structure of Weighted Composition Operators from Bloch Type Spaces to the Disk Algebra[J]. 2021, 38(3): 62-64.
许丽葵, 邓秀勤, 刘军明. 加权复合算子从Bloch型空间到圆盘代数的拓扑结构[J]. 广东工业大学学报, 2021, 38(3): 62-64. DOI： 10.12052/gdutxb.200092.

Xu Li-kui, Deng Xiu-qin, Liu Jun-ming. The Topological Structure of Weighted Composition Operators from Bloch Type Spaces to the Disk Algebra[J]. 2021, 38(3): 62-64. DOI： 10.12052/gdutxb.200092.

摘要

设

$ A$

img text_id='M1' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M1.jpg'>

为圆盘代数

$ u$

img text_id='M2' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M2.jpg'>

和

$ \varphi $

img text_id='M3' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M3.jpg'>

是

$ A$

img text_id='M1' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M1.jpg'>

上的解析函数

刻画了加权复合算子

$ u{C_\varphi }$

img text_id='M5' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M5.jpg'>

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。

Abstract

Let

$ A$

img text_id='M6' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M6.jpg'>

be the disk algebra

$ u$

img text_id='M7' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M7.jpg'>

and

$ \varphi $

img text_id='M8' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M8.jpg'>

be analytic functins on

some estimates of weighted composition operators

$ u{C_\varphi }$

img text_id='M9' class='formula-img' style='display:none;' src='gdgydxxb-38-3-62_M9.jpg'>

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.

关键词

Keywords

references

ZHU K. Bloch type spaces of analytic functions [J]. The Rocky Mountain Journal of Mathematics, 1993, 23(3): 1143-1177.

ZHU K. Operator theory in function spaces[M]. 2nd ed. Providence: Mathematical Surveys and Monographs, 2007.

CONTRERAS M D, HERNÁNDEZ-DÍAZ A G. Weighted composition operators on Hardy spaces [J]. Journal of Mathematical Analysis and Applications, 2001, 263(1): 224-233.

ČUČKOVIÓ Z, ZHAO R. Weighted composition operators on the Bergman space [J]. Journal of the London Mathematical Society, 2004, 70(2): 499-511.

IZUCHI K, OHNO S. Topological structure of the space of weighted composition operators between different Hardy spaces [J]. Integral Equations Operator Theory, 2014, 80(2): 153-164.

HOSOKAWA T, IZUCHI K, ZHENG D. Isolated points and essential components of composition operators on H ∞ [J ] . Proceeding of the American Mathematical Society, 2002, 130(6): 1765-1773.

FANG Z, ZHOU Z. The topological structure of weighted composition operators from Lipschitz spaces to H ∞ [J ] . Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42(3): 897-908.

ZHANG X J. Boundedness of weighted composition operators on -Bloch spaces on the unit ball of C n [J ] . Journal of Mathematical Study, 2003, 36(3): 243-250.

MANHAS J, ZHAO R. New estimates of essential norms of weighted composition operators between Bloch type spaces [J]. Journal of Mathematical Analysis and Applications, 2012, 389(1): 32-47.

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