On quasi-affinity and reducing subspaces of multiplication operator on a certain closed subspace

Abstract

Let H denote a certain closed subspace of the Bergman space A 2 α(Bn)(α > −1) of the unit ball in C n . In this paper, we prove that the operator ⊕m 1 Mz (s1,··· ,sn) is quasi-affine to the multiplication operator Mz (ms1,···,msn) on H . Furthermore, the reducing subspaces of Mz (ms1,··· ,msn) are characterized on H .