A criterion on the hyponormality of Toeplitz operators with polynomial symbols via Schur numbers

In this paper we give a complete characterization on the hyponormality of the Toeplitz operators Tφ with trigonometric polynomial symbols (g,h∈H2) when g divides h. This is accomplished by using a criterion on the contractivity of the inverse of a lower triangular (finite) Toeplitz matrix via Schur numbers of an induced analytic polynomial.