The invariant subspaces of $S\oplus S^{\ast }$

Abstract

Using the tools of Sz.-Nagy--Foias theory of contractions, we describe in detail the invariant subspaces of the operator $S\oplus S^{\ast }$, where $S$ is the unilateral shift on a Hilbert space. This answers a question of Câmara and Ross.

11 pages. Theorem 4.4 corrected