Dirichlet空间上一类乘法算子的相似性  

Similarity of a Class of Multiplication Operators on Dirichlet Space

作　　者：秦春桃 陈泳 QIN Chuntao;CHEN Yong(Department of Foundational Teaching, Hope College of Southwest Jiaotong University, Chengdu 610400, China;Department of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

机构地区：[1]西南交通大学希望学院基础教学部,四川成都610400 [2]杭州师范大学数学系,浙江杭州311121

出　　处：《湖州师范学院学报》2020年第2期1-4,共4页Journal of Huzhou University

基　　金：国家自然科学基金项目(11771401)。

摘　　要：利用Dirichlet函数表示方法,证明在Dirichlet空间上以n阶有限Blaschke积?为符号的乘法算子M?相似等价于Mz■In,由此证得与Mz■In相似等价的乘子只有n阶有限Blaschke积为符号的乘法算子.In this paper,it is proved that on the Dirichlet space,the multiplication operator M? with finite Blaschke product ? with order n is similarly equivalent to Mz■In and the latter one is similarly equivalent to a multiplier M? only if ? is a finite Blaschke product with order n.

关 键 词：DIRICHLET空间 乘法算子 相似性 有限Blaschke积 

分 类 号：O177.1[理学—数学]