Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

HYPONORMALITY OF TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES

  • Lee, Jongrak (Department of Mathematics, Sungkyunkwan University) ;
  • Lee, Youho (Department of Internet Information, Daegu Haany University)
  • Received : 2013.04.25
  • Accepted : 2013.05.20
  • Published : 2013.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this note we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Weighted Bergman space $A^2_{\alpha}(\mathbb{D})$ with symbol in the class of functions $f+\bar{g}$ with polynomials $f$ and $g$ of degree 2.

Keywords

References

  1. C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), 809-812. https://doi.org/10.1090/S0002-9939-1988-0947663-4
  2. R.E. Curto, I.S. Hwang and W.Y. Lee, Hyponormality and subnormality of block Toeplitz operators, Adv. Math. 230 (2012), 2094-2151. https://doi.org/10.1016/j.aim.2012.04.019
  3. R.E. Curto and W.Y. Lee, Joint hyponormality of Toeplitz pairs, Memoirs Amer. Math. Soc. 150(712) (2001).
  4. I.S. Hwang, I.H. Kim and W.Y. Lee, Hyponormality of Toeplitz operators with polynomial symbol, Math. Ann 313 (1999), 247-261. https://doi.org/10.1007/s002080050260
  5. I.S. Hwang and W.Y. Lee, Hyponormality of trigonometric Toeplitz operators, Trans. Amer. Math. 354 (2002), 2461-2474. https://doi.org/10.1090/S0002-9947-02-02970-7
  6. I.S. Hwang and J.R. Lee, Hyponormal Toeplitz operators on the weighted Bergman spaces, Math. Ineq. and App. 15 (2012), 323-330.
  7. Yufeng Lu and Chaomei Liu, Commutativity and hyponormality of Toeplitz operators on the weighted Bergman space, J. Korean Math. Soc. 46 (2009), 621-642. https://doi.org/10.4134/JKMS.2009.46.3.621
  8. 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
  9. D. Sarason, Generalized interpolation in $H^{\infty}$, Trans. Amer. Math. Soc. 127 (1967), 179-203.
  10. K. Zhu, Hyponormal Toeplitz operators with polynomial symbols, Integral Equations and Operator Theory 21 (1995), 376-381. https://doi.org/10.1007/BF01299971

Cited by

  1. Hyponormal Toeplitz operators with polynomial symbols on weighted Bergman spaces vol.2014, pp.1, 2014, https://doi.org/10.1186/1029-242X-2014-335