THE SEMI-COMMUTATOR OF TOEPLITZ OPERATORS ON THE BIDISC

CAIXING GU DECHAO ZHENG

Abstract. In this paper we characterize when the semi-commutator T_{f}T_{g} − T_{fg} of two Toeplitz operators T_{f} and T_{g} on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T^{2} are given.