The Hyponormal Toeplitz operators on the vector valued Bergman space
Bull. Korean Math. Soc. 2014 Vol. 51, No. 1, 237-252
https://doi.org/10.4134/BKMS.2014.51.1.237
Printed January 1, 2014
Yufeng Lu, Puyu Cui, and Yanyue Shi
Dalian University of Technology, Dalian University of Technology, Ocean University of China
Abstract : In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where $\Phi = F + G^\ast$, $ F(z), \ G (z)$ are some matrix valued polynomials on the vector valued Bergman space $L^2_a (\mathbb{D},\mathbb{C}^n )$. We also show some necessary conditions for the hyponormality of $T_{F + G^\ast}$ with $F + G^\ast \in h^\infty \otimes M_{n \times n }$ on $L^2_a (\mathbb{D},\mathbb{C}^n )$.
Keywords : hyponormality, block Toeplitz operator, block Hankel operator
MSC numbers : 47B38
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