호남수학학술지 (Honam Mathematical Journal)

  • 제40권1호
  • /
  • Pages.155-162
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  • 2018
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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HYPONORMAL TOEPLITZ OPERATORS ON THE HARDY SPACE OF THE UNIT CIRCLE

  • Kwon, Eun Young (Department of Mathematics, Changwon National University) ;
  • Kim, An Hyun (Department of Mathematics, Changwon National University)
  • 투고 : 2017.12.10
  • 심사 : 2017.12.27
  • 발행 : 2018.03.25
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초록

In this paper, we are concerned with hyponormal Toeplitz operators on the Hardy space of the unit circle. Our main result of this paper is to provide a simple and transparent proof on the hyponormality of Toeplitz operators with symmetric-type symbols via Schur complement lemma.

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과제정보

연구 과제 주관 기관 : Changwon National University

참고문헌

  1. M. Cho, R. E. Curto and W. Y. Lee, Triangular Toeplitz contractions and Cowen sets for analytic polynomials, Proc. Amer. Math. Soc. 130 (2002), 3957-3604.
  2. C. C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), 809-812. https://doi.org/10.1090/S0002-9939-1988-0947663-4
  3. R. E. Curto and W. Y. Lee, Joint hyponormality of Toeplitz pairs, Memoirs Amer. Math. Soc. no. 712, Amer. Math. Soc., Providence, 2001.
  4. I. Gohberg, S. Goldberg and M.A. Kaashoek, Classes of Linear Operators, Vol II, Birkhauser Verlag, Basel, 1993.
  5. I. S. Hwang and W. Y. Lee, Hyponormality of Toeplitz operators with polynomial and symmetric-type symbols, Integral Equations and Operator Theory 50(3) (2004), 363-373. https://doi.org/10.1007/s00020-002-1235-3
  6. T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Amer. Math. Soc. 338 (1993), 753-769. https://doi.org/10.1090/S0002-9947-1993-1162103-7
  7. I. Schur, Uber Potenzreihen, die im Innern des Einheitskreises Beschrankt sind [I], Journal fur die reine und angewandte Mathematik 147 (1917), 205-232.