Let $T\colon l^2(\mathbb{Z})\to l^2(\mathbb{Z})$ be right shift operator. I was asked to prove that there are uncountably many $T$-invariant closed subspaces. The only invariant subspaces I can think of is having $0$ in before $n^{th}$ entry. But these only gives me countably many invariant subspaces.
I tried using isomorphism between $l^2(\mathbb{Z})$ and $L^2(S^1)$ and view $T$ as multiplication by $z$ operator but could not progress.
Any help would be appreciated.