Hyponormality of Toeplitz Operators on the Dirichlet Space  

作　　者：Qiao Fei LU Tao YU 

机构地区：[1]Department of Mathematics,Zhejiang Normal University,Zhejiang 321004,P.R.China

出　　处：《Journal of Mathematical Research and Exposition》2011年第6期1057-1063,共7页数学研究与评论（英文版）

基　　金：Supported by the National Natural Science Foundation of China (Grant No.10971195);the Natural Science Foundation of Zhejiang Province (Grant Nos.Y6090689; Y6110260)

摘　　要：In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.

关 键 词：Toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space 

分 类 号：O177.1[理学—数学] O177.3[理学—基础数学]