Completely Non-Normal Toeplitz Operators
Received:October 23, 2009  Revised:January 18, 2010
Key Word: Toeplitz operator   completely non-normal   hyponormal   cyclic.
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.10971020; 10671028).
 Author Name Affiliation Yan Yue SHI School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China Yu Feng LU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
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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.