A gap between hyponormality and subnormality for block Toeplitz operators

This paper concerns a gap between hyponormality and subnormality for block Toeplitz operators. We show that there is no gap between 2-hyponormality and subnormality for a certain class of trigonometric block Toeplitz operators (e.g., its co-analytic outer coefficient is invertible). In addition we consider the extremal cases for the hyponormality of trigonometric block Toeplitz operators: in this case, hyponormality and normality coincide.