多圆柱上Dirichlet空间中Toeplitz算子的交换性  

Commuting Toeplitz operators on the Dirichlet space of the ploydisk

作　　者：耿立刚[1] 周泽华[1] 

机构地区：[1]天津大学数学系,天津300072

出　　处：《中国科学：数学》2010年第5期437-445,共9页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10971153;10671141)资助项目

摘　　要：本文讨论了多圆柱上Dirichlet空间中的正规Toeplitz算子以及全纯指标和反全纯指标的两个Toeplitz算子的交换性.我们证明具有多圆柱上Dirichlet空间中反全纯指标的两个Toeplitz算子可交换当且仅当两个指标是线性相关的,同时证明全纯指标和反全纯指标的两个Toeplitz算子可交换当且仅当两个指标有一个是常数.In this paper,we completely characterize the normal Toeplitz operator and commutator of two Toeplitz operators with conjugate holomorphic or holomorphic symbols on the Dirichlet space of the polydisk. We show that the two Toeplitz operators with conjugate holomorphic symbols are commute on the Dirichlet space of polydisk if and only if two symbols are linearly dependent,and also prove that Toeplitz operator with holomorphic symbol and Toeplitz operator with conjugate holomorphic symbol are commute if and only if one of the two symbols is a constant.

关 键 词：TOEPLITZ算子 DIRICHLET空间 多圆柱 全纯指标 反全纯指标 

分 类 号：O177[理学—数学]