Dirichlet空间上一类积分算子的约化子空间

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 595-602.

Dirichlet空间上一类积分算子的约化子空间

张核心()

^{河北师范大学数学科学学院石家庄 050024}

收稿日期:2020-03-20 出版日期:2021-06-26 发布日期:2021-06-09
作者简介:张核心, E-mail: corehebtu@126.com
基金资助:
河北师范大学研究生创新资助项目(CXZZSS2020052)

On Reducing Subspaces of a Class of Integral Operator on Dirichlet Spaces

Hexin Zhang()

^{School of Mathematical and Sciences, Hebei Normal University, Shijiazhuang 050024}

Received:2020-03-20 Online:2021-06-26 Published:2021-06-09
Supported by:
the Postgraduate Innovative Funding Project of Hebei Normal University(CXZZSS2020052)

摘要/Abstract

摘要：

刻画了n移位算子加带特定权的Volterra算子T₁在Dirichlet空间上的相似性，利用算子理论技巧证明了 $T_{1}$ 在Dirichlet空间上的作用和乘法算子 $M_{p}$ 在空间 $S（{\Bbb D}）$ 上的作用相似，进一步证明了当 $p（z）=z^{n}$ 时相应的算子 $T_{2}$ 有 $2^{n}$ 个约化子空间.

关键词: Dirichlet空间, Volterra算子, n移位算子, 约化子空间

Abstract:

We characterize the similarity of $n$ -shift plus certain weighted Volterra operator denoted by $T_{1}$ on the Dirichlet space ${\cal D}$ , and prove that $T_{1}$ acting on ${\cal D}$ is similar to the multiplication operator $M_{p}$ acting on $S({\Bbb D})$ by using some techniques in operator theory. Furthermore, we consider the case of $p(z)=z^{n}$ corresponding to the operator $T_{2}$ , and prove that the operator $T_{2}$ has exactly $2^{n}$ reducing subspaces.

Key words: Dirichlet space, Volterra operator, n-Shift operator, Reducing subspaces

中图分类号:

O177.2

张核心. Dirichlet空间上一类积分算子的约化子空间[J]. 数学物理学报, 2021, 41(3): 595-602.

Hexin Zhang. On Reducing Subspaces of a Class of Integral Operator on Dirichlet Spaces[J]. Acta mathematica scientia,Series A, 2021, 41(3): 595-602.

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