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Hyponormality of Toeplitz Operators on the Dirichlet Space

Hyponormality of Toeplitz Operators on the Dirichlet Space
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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.
作者 Qiao Fei LU Tao YU
机构地区 Department of Mathematics
出处 《Journal of Mathematical Research and Exposition》 CSCD 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)
关键词 Toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space Toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space
分类号 O177.1 [理学—基础数学] O177.3 [理学—基础数学]
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Journal of Mathematical Research and Exposition
2011年 第6期

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