Algebraic properties of quasihomogeneous and separately quasihomogeneous Toeplitz operators on the pluriharmonic Bergman space (Q2015268)

Summary: We study some algebraic properties of Toeplitz operator with quasihomogeneous or separately quasihomogeneous symbol on the pluriharmonic Bergman space of the unit ball in \(\mathbb C^n\). We determine when the product of two Toeplitz operators with certain separately quasi-homogeneous symbols is a Toeplitz operator. Next, we discuss the zero-product problem for several Toeplitz operators, one of whose symbols is separately quasihomogeneous and the others are quasi-homogeneous functions, and show that the zero-product problem for two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary. Finally, we also characterize the commutativity of certain quasihomogeneous or separately quasihomogeneous Toeplitz operators.