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THE HYPONORMAL TOEPLITZ OPERATORS ON THE VECTOR VALUED BERGMAN SPACE
Lu, Yufeng,Cui, Puyu,Shi, Yanyue Korean Mathematical Society 2014 대한수학회보 Vol.51 No.1
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, 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 $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.
The Hyponormal Toeplitz operators on the vector valued Bergman space
Yufeng Lu,Puyu Cui,Yanyue Shi 대한수학회 2014 대한수학회보 Vol.51 No.1
In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ 2 h∞ ⓧ Mn×n on L2 a(D, Cn). In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators TΦ, where Φ = F +G∗, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space L2 a(D, Cn). We also show some necessary conditions for the hyponormality of TF+G* with F + G∗ ∈ h∞ ⓧ Mn×n on L2 a(D, Cn).