## Hyponormality of trigonometric Toeplitz operators

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- by In Sung Hwang and Woo Young Lee PDF
- Trans. Amer. Math. Soc.
**354**(2002), 2461-2474 Request permission

## 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.## References

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## Additional Information

**In Sung Hwang**- Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
- MR Author ID: 628053
- Email: ishwang@math.skku.ac.kr
**Woo Young Lee**- Affiliation: Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Korea
- MR Author ID: 263789
- Email: wylee@yurim.skku.ac.kr
- 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.
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 2461-2474 - MSC (2000): Primary 47B20, 47B35
- DOI: https://doi.org/10.1090/S0002-9947-02-02970-7
- MathSciNet review: 1888332

Dedicated: Dedicated to Professor Yong Tae Kim on his 65th birthday