On quasi-similarity and reducing subspaces of multiplication operator on the Fock space

Let Fα2(α>0) denote the Fock space which consists of all entire functions ff in L2(C,dλα)L2(C,dλα). We prove that the multiplication operator MznMzn is quasi-similar to ⨁1nMz on Fα2. Then the reducing subspaces of MznMzn are characterized on Fα2.