Reducing Subspaces of Toeplitz Operators on N_φ-type Quotient Modules on the Torus

摘要

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ(z) on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H2(Γω) Θφ(ω)H 2 (Γω). Moreover, the restriction of Sψ(z) on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.