We discuss balicki stick some algebraic properties of Toeplitz operators on the Bergman space of the polydisk Dn.Firstly, we introduce Toeplitz operators with quasihomogeneous symbols and property (P).Secondly, we study commutativity of certain quasihomogeneous Toeplitz operators and commutators of diagonal Toeplitz operators.Thirdly, PTO Clutches we discuss finite rank semicommutators and commutators of Toeplitz operators with quasihomogeneous symbols.
Finally, we solve the finite rank product problem for Toeplitz operators on the polydisk.