DOI QR코드

DOI QR Code

HYPONORMALITY OF TOEPLITZ OPERATORS WITH POLYNOMIAL SYMBOLS

  • Kim, Jae Myung (Department of Mathematics Sungkyunkwan University) ;
  • Lee, Youho (Department of Internet Information Daegu Hanny University)
  • Received : 2010.12.16
  • Accepted : 2011.02.15
  • Published : 2011.03.30

Abstract

In this note we present some necessary and sufficient conditions for the hyponormality of Toeplitz operators $T_{\varphi}$ under certain assumptions concerning the trigonometric polynomial symbol ${\varphi}$.

Keywords

References

  1. A. Brown and P.R. Halmos, Algebraic properties of Toeplitz operators, J. Reine Angew. Math. 213 (1963/1964), 89-102.
  2. 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. P. Fan, Remarks on hyponormal trigonometric Toeplitz operators, Rocky Mountain J. Math. 13 (1983), 489-493. https://doi.org/10.1216/RMJ-1983-13-3-489
  4. D.R. Farenick and W.Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), 4153-4174. https://doi.org/10.1090/S0002-9947-96-01683-2
  5. I. Gohberg, S. Goldberg and M.A. Kaashoek, Classes of Linear Operators, Vol II, Birkhauser Verlag Basel. (1993).
  6. I. S. Hwang and W.Y. Lee, Hyponormality of trigonometric Toeplitz operators, Trans. Amer. Math. Soc. 354 (2002), 2461-2474. https://doi.org/10.1090/S0002-9947-02-02970-7
  7. 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
  8. I. Schur, Uber Potenzreihen die im Innern des Einheitskreises beschrankt sind, J. Reine Angew. Math. 147 (1917), 205-232