THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE

Title & Authors
THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE
Lu, Yufeng; Cui, Puyu; Shi, Yanyue;

Abstract
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $\small{T_{\Phi}}$, where $\small{{\Phi}}$
Keywords
hyponormality;block Toeplitz operator;block Hankel operator;
Language
English
Cited by
References
1.
P. Ahern and Z. Cuckovic, A mean value inequality with applications to Bergman space operators, Pacific J. Math. 173 (1996), no. 2, 295-305.

2.
C. Cowen, Hyponormality of Toeplitz operators, Proc. Amer. Math. Soc. 103 (1988), no. 3, 809-812.

3.
R. E. Curto, I. S. Hwang, and W. Y. Lee, Hyponormality and subnormality of block Toeplitz operators, Adv. Math. 230 (2012), no. 4-6, 2094-2151.

4.
D. R. Farenick and W. Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), no. 10, 4153-4174.

5.
C. Gu, J. Hendricks, and D. Rutherford, Hyponormality of block Toeplitz operators, Pacific J. Math. 223 (2006), no. 1, 95-111.

6.
C. Gu and J. E. Shapiro, Kernels of Hankel operators and hyponormality of Toeplitz operators, Math. Ann. 319 (2001), no. 3, 553-572.

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

9.
I. S. Hwang and J. Lee, Hyponormal Toeplitz operators on the Bergman space. II, Bull. Korean Math. Soc. 44 (2007), no. 3, 517-522.

10.
Y. F. Lu and Y. Y. Shi, Hyponormal Toeplitz operators on the weighted Bergman space, Integral Equations Operator Theory 65 (2009), 115-129.

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

12.
K. H. Zhu, Hyponormal Toeplitz operators with polynomial symbols, Integral Equations Operator Theory 21 (1995), no. 3, 376-381.