Hyponormality of block Toeplitz operators on the weighted Bergman spaces

In this paper we consider the block Toeplitz operators TPhi on the weighted Bergman space Aα2(D,Cn) and we give a necessary and sufficient condition for the hyponormality of block Toeplitz operators with symbol in the class of functions Φ=F+G* with matrix-valued polynomial functions F and G with degree 2.