(untitled) (Communications in Mathematical Research, 2021)
In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol S_ψ(z) on N_ϕ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2(Γ_ω) ⊖ ϕ(ω)H^2 (Γ_ω). Moreover, the restriction of S_ψ(z) on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift M_z.