Abstract. In this note we give several examples related to products of Toeplitz operators on the Bergman space. If $f$, $g$, and $h$ are symbols, we say that $T_fT_g=T_h$ in a non-trivial way if neither $\overline f$ nor $g$ is holomorphic. It is known that such triples exist. We give a method to construct many such examples. We show that it is also possible to have $T_fT_g=T_{fg}$ or $T_fT_g=I$ in a non-trivial way. We also have some positive results on products of Toeplitz operators.

AMS Subject Classification (1991): 47B35

Received April 25, 2003, and in revised form September 24, 2003. (Registered under 5819/2009.)