商模N_φ上解析Toepltz算子的约化子空间

Reducing subspace of analytic Toeplitz operators on N_φ-quotient module

假设T^n表示多圆盘,H^2(T^n)表示T^n上的Hardy空间.K表示H^2(T^n)中由{(z_1-φ(z_2))f_1+…+(z_1-φ(z_n))f_(n-1):f_i∈H^2(T^n),1≤i≤n-1}生成的子模, N_φ表示K在H^2(T^n)中的商模.则N_φ上以有限Blaschke乘积ψ(z)为符号的Toeplitz型算子T_ψ是可约的.

Let T^n be the polydisc in C^n, H^2（T^n）be the Hardy space on D^n. Suppose that K is the submodule of H^2（D^n） generated by {（z1 -Ф（z2））f1＋…＋（z1 -Ф（zn））fn-1 ： fi∈ H^2（T^n）, 1 ≤i≤n-1}, NФ is the quotient module of K in H^2（T^n）.Then analytic Toeplitz operators Tψ with finite Blaschke product ψ as symbol are reducible.