Hilbert-Schmidtness of some finitely generated submodules in H2(D2)

$$N_{\psi }$$-Type Quotient Modules in $$H^{2}({\mathbb {D}}^{n})$$

“…Wu and Xu [15] studied the reducing subspaces of these quotient modules. Luo et al [12] proved that every finitely generated submodule M containing z 1 − ψ(z 2 ) is Hilbert-Schmidt, where ψ is any finite Blaschke product. Wu and Yu [16] studied the essential spectrum and essential normality of the quotient module Duan [4] proved the essential normality of quotient modules…”