Toeplitz operators with quasihomogeneous symbols on the Bergman space of the unit ball (Q1757907)

The authors study some algebraic properties of Toeplitz operators with quasihomogeneous symbols acting on the Bergman space over the unit ball. Their main results characterize the finite rank semicommutators and commutators of the above Toeplitz operators. Under different conditions on the defining quasihomogeneous symbols, the authors show that there are no such nontrivial finite rank semicommutators and commutators: either they are zero, or one of the Toeplitz operators has to be zero.