Multipliers of a Wandering Subspace for a Shift Invariant Subspace II

Abstract

Let $M$ be a shift invariant subspace in the two variable Hardy space $H^2(\Gamma_z\times\Gamma_w)$. We study $\mathcal{M}(M_z)=\{\phi\in H^\infty(\Gamma_z\times \Gamma_w) : \phi M_z\subseteq M_z\}$ where $M_z=M\ominus zM$. We give several sufficient conditions for $\mathcal{M}(M_z)=H^\infty(\Gamma_w)$ where $H^\infty(\Gamma_w)$ is the one variable Hardy space.