Rank of a co-doubly commuting submodule is 2

Arup Chattopadhyay, B. Krishna Das, Jaydeb Sarkar

We prove that the rank of a non-trivial co-doubly commuting submodule is $2$. More precisely, let $\phi ,\psi \in H^{\infty }(\mathbb{D})$ be two inner functions. If $\mathcal{Q}_φ = H^2(\ma…