Algebraic properties of Toeplitz operators on the pluriharmonic Bergman space (Q1951075)

The authors study a number of algebraic properties of Toeplitz operators with radial and/or quasihomogeneous symbols acting on the pluriharmonic Bergman space over the unit ball. The questions under study include a criterion for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator, the zero-product problem for several Toeplitz operators with radial symbols, the finite rank product problem of a finite number of Toeplitz operators with quasihomogeneous symbols, the finite rank commutators and semicommutators problem for two Toeplitz operators with quasihomogeneous symbols.