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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
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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.

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