| Hyponormality of Toeplitz Operators on the Dirichlet Space |
| Received:June 01, 2010 Revised:January 12, 2011 |
| Key Words:
Toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10971195) and the Natural Science Foundation of Zhejiang Province (Grant Nos.Y6090689; Y6110260). |
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| Abstract: |
| In this paper, we prove that the necessary and sufficient condition for a Toeplitz operator $T_u$ 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. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.06.013 |
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