TY - JOUR
T1 - Reducing Subspaces of Toeplitz Operators on $N_ϕ$-Type Quotient Modules on the Torus
AU - Wu , Yan
AU - Xu , Xianmin
JO - Communications in Mathematical Research 
VL - 1
SP - 19
EP - 29
PY - 2021
DA - 2021/05
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19071.html
KW - module, $N_ϕ$-type quotient module, the analytic Toeplitz operator, reducing subspace, finite Blaschke product
AB - <p style="text-align: justify;">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 $M_z$.</p>