Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

  • Published : 2008.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we consider the hyponormality of Toeplitz operators $T_{\varphi}$ on the Bergman space $L_a^2{(\mathbb{D})$ in the cases, where ${\varphi}\;:=f+\bar{g}$ (f and g are polynomials). We present some necessary or sufficient conditions for the hyponormality of $T_{\varphi}$ under certain assumptions about the coefficients of ${\varphi}$.

Keywords

References

  1. S. Axler, Bergman spaces and their operators, Surveys of some recent results in operator theory, Vol. I, 1-50, Pitman Res. Notes Math. Ser., 171, Longman Sci. Tech., Harlow, 1988
  2. C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), no. 3, 809-812 https://doi.org/10.2307/2046858
  3. R. E. Curto and W. Y. Lee, Joint hyponormality of Toeplitz pairs, Mem. Amer. Math. Soc. 150 (2001), no. 712, x+65 pp
  4. R. Douglas, Banach Algebra Techniques in Operator Theory, Pure and Applied Mathematics, Vol. 49. Academic Press, New York-London, 1972
  5. P. Duren, Theory of $H^{p}$ Spaces, Pure and Applied Mathematics, Vol. 38 Academic Press, New York-London 1970
  6. D. R. Farenick and W. Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), no. 10, 4153-4174 https://doi.org/10.1090/S0002-9947-96-01683-2
  7. I. S. Hwang, Hyponormal Toeplitz operators on the Bergman space, J. Korean Math. Soc. 42 (2005), no. 2, 387-403 https://doi.org/10.4134/JKMS.2005.42.2.387
  8. I. S. Hwang, I. H. Kim, and W. Y. Lee, Hyponormality of Toeplitz operators with polynomial symbols, Math. Ann. 313 (1999), no. 2, 247-261 https://doi.org/10.1007/s002080050260
  9. I. S. Hwang and W. Y. Lee, Hyponormality of trigonometric Toeplitz operators, Trans. Amer. Math. Soc. 354 (2002), no. 6, 2461-2474 https://doi.org/10.1090/S0002-9947-02-02970-7
  10. T. Nakazi and K. Takahashi, Hyponormal Toeplitz operators and extremal problems of Hardy spaces, Trans. Amer. Math. Soc. 338 (1993), no. 2, 753-767 https://doi.org/10.2307/2154427
  11. H. Sadraoui, Hyponormality of Toeplitz operators and composition operators, Thesis, Purdue University, 1992

Cited by

  1. Hyponormality of Toeplitz operators in several variables by the weighted shifts approach pp.1563-5139, 2020, https://doi.org/10.1080/03081087.2018.1556241
  2. Hyponormal Toeplitz operators with non-harmonic algebraic symbol pp.1664-235X, 2019, https://doi.org/10.1007/s13324-018-00279-2