Cyclicity of reproducing kernels in weighted Hardy spaces over the bidisk

A Brief Survey of Operator Theory in H 2(𝔻2)

“…The space M ⊖ (z 1 M + z 2 M) is sometimes called the defect space for the submodule M and its importance will become evident later. Its dimension is less than or equal to the rank of M ( [36] Theorem 3.6 (Izuchi [59]). There exists a nontrivial function…”