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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hyponormality of trigonometric Toeplitz operators


Authors: In Sung Hwang and Woo Young Lee
Journal: Trans. Amer. Math. Soc. 354 (2002), 2461-2474
MSC (2000): Primary 47B20, 47B35
Published electronically: February 14, 2002
MathSciNet review: 1888332
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Abstract: In this paper we establish a tractable and explicit criterion for the hyponormality of arbitrary trigonometric Toeplitz operators, i.e., Toeplitz operators $T_{\varphi }$ with trigonometric polynomial symbols $\varphi $. Our criterion involves the zeros of an analytic polynomial $f$ induced by the Fourier coefficients of $\varphi $. Moreover the rank of the selfcommutator of $T_{\varphi }$ is computed from the number of zeros of $f$ in the open unit disk $\mathbb{D}$ and in $\mathbb{C}\setminus \overline{\mathbb{D}}$ counting multiplicity.


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Additional Information

In Sung Hwang
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Email: ishwang@math.skku.ac.kr

Woo Young Lee
Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
Email: wylee@yurim.skku.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9947-02-02970-7
PII: S 0002-9947(02)02970-7
Keywords: Trigonometric Toeplitz operators, hyponormal operators
Received by editor(s): October 19, 2000
Published electronically: February 14, 2002
Additional Notes: This work was partially supported by KOSEF research project No. R01-2000-00003.
Dedicated: Dedicated to Professor Yong Tae Kim on his 65th birthday
Article copyright: © Copyright 2002 American Mathematical Society