Invariant subspaces of contractions with constant characteristic function

We describe all the invariant subspaces of a completely nonunitary contraction T c T_c with nonzero scalar constant characteristic function c c , where | c | > 1 |c|>1 . Moreover, we show that T c T_c and restriction to its invariant subspaces are essentially normal. Using this description of T c T_c -invariant subspaces, we then identify the hyperinvariant subspaces.