The Hyponormal Toeplitz operators on the vector valued Bergman space

摘要

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{Phi}$, where $Phi = F + G^st$, $ 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 $T_{F + G^st}$ with $F + G^st in h^infty otimes M_{n imes n }$ on $L^2_a (mathbb{D},mathbb{C}^n )$.