| Completely Non-Normal Toeplitz Operators |
| Received:October 23, 2009 Revised:January 18, 2010 |
| Key Words:
Toeplitz operator completely non-normal hyponormal cyclic.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10971020; 10671028). |
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| Abstract: |
| In this paper, we show that the hyponormal Toeplitz operator $T_{\varphi}$ with trigonometric polynomial symbol $\varphi$ is either normal or completely non-normal. Moreover, if $T_\varphi$ is non-normal, then $T_{\bar{\varphi}}$ has a dense set of cyclic vectors. Some general conditions are also considered. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2011.04.019 |
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