Common invariant subspaces of two doubly commuting operators on $\ell^2 \otimes \mathbb{C}^2$

Abstract

In this paper, we study common invariant subspaces of $\mathbb{T}$ and $\mathbb{S}$ on $\ell^2 \otimes \mathbb{C}^2$ where $\mathbb{T} = T \otimes I_{\mathbb{C}^2}$ and $\mathbb{S} = I_{\ell^2} \otimes S$. We describe such invariant subspaces using $T$ and $S$.