Algebraic Properties of Toeplitz Operators on the Polydisk

الملخص EN

We discuss 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, 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.