A Generalization of Cowen′s Characterization of Hyponormal Toeplitz Operators

In this paper we extend an elegant result of C. C. Cowen [Proc. Amer. Math. Soc.103 (1988), 809-812] on the hyponormality of Toeplitz operators to a class of (generalized) Toeplitz operators. In order to do this by a commutant lifting approach we study the operator equation HA = HBTC, where HA, HB are (generalized) Hankel operators and TC is an analytic Toeplitz operator. Related results about the range inclusion of Hankel and Toeplitz operators are also obtained.