Rank-one commutators on invariant subspaces of the Hardy space on the bidisk III

Abstract

We study a special type of invariant subspaces ${\mathcal M}$ on the bidisk which are studied in the previous papers. We determine the rank of cross commutators on $H^2\ominus {\mathcal M}$, and study when ${\mathcal M}$ is generated by ${\mathcal M}\ominus (z{\mathcal M}+w{\mathcal M})$ as an invariant subspace of $H^2$.