Dirichlet空间上的复合算子  

Composition Operators on Dirichlet Space

作　　者：李金燕[1] 刘丹[1] LI Jinyan;LIU Dan(College of Mathematics and Informatics,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]华南农业大学数学与信息学院,广州510642

出　　处：《四川轻化工大学学报（自然科学版）》2021年第6期92-97,共6页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金项目(11701188)。

摘　　要：函数空间上的算子理论一直是泛函分析的重要研究课题,与数学的许多领域有着密切的联系。复合算子架起了解析函数论和算子理论之间的桥梁。设φ是解析映射,将一个解析函数f映射成f∘φ的算子C_(φ)称为复合算子。由于诱导函数φ的函数性质与复合算子C_(φ)的算子性质之间关系紧密,因此复合算子的研究备受广大学者的青睐。首先研究了经典Dirichlet空间D上紧复合算子C_(φ)的性质,通过Denjoy-Wolff定理讨论了单位圆盘上的解析自映射φ的不动点,利用φ的不动点对紧复合算子的谱进行了计算;其次,利用计数函数n_(φ)(w)对D上有界复合算子的范数和本性范数进行了估计;最后,结合D上的再生核给出了有界复合算子是正规算子的等价刻画。Operator theory in function space has always been an important research topic in functional analysis,and has close relationship with many fields of mathematics.Composition operators have built a bridge between analytic function theory and operator theory.Letφbe analytic mapping,and the operator C_(φ) that maps an analytic function f to f∘φis called composition operator.Because of the close relationship between the functional properties of induced functionφand the properties of composition operators C_(φ),the research on composition operators is favored by the majority of scholars.Firstly,the compact composition operators C_(φ) on the classical Dirichlet space Dare studied.In this paper,the fixed point of analytic self mapping on the unit disk is discussed by using Denjoy-Wolff theorem,and the spectra of compact composition operators is calculated by using the fixed points ofφ.Then,the norms and essential norms of bounded composition operators on D are estimated by using the counting function n_(φ)(w).Finally,the equivalent conditions for bounded composition operators to be normal operators are given by using the reproducing kernel on D.

关 键 词：DIRICHLET空间 复合算子 谱 本性范数 正规算子 

分 类 号：O177[理学—数学]