HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE

Title & Authors
HYPONORMALITY OF TOEPLITZ OPERATORS ON THE BERGMAN SPACE
Hwang, In-Sung;

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

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

7.
I. S. Hwang, Hyponormal Toeplitz operators on the Bergman space, J. Korean Math. Soc. 42 (2005), no. 2, 387-403

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

9.
I. S. Hwang and W. Y. Lee, Hyponormality of trigonometric Toeplitz operators, Trans. Amer. Math. Soc. 354 (2002), no. 6, 2461-2474

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

11.
H. Sadraoui, Hyponormality of Toeplitz operators and composition operators, Thesis, Purdue University, 1992