Invariant subspaces of the Cesàro operator

This paper explores various classes of invariant subspaces of the classical Cesàro operator C on the Hardy space H 2 . We provide a characterization of the finite co-dimensional C -invariant subspaces, based on earlier work of the first two authors, and determine exactly which model spaces are C -invariant subspaces; using this, we describe the C -invariant subspaces contained in model spaces, which we show are all cyclic. Along the way, we re-examine an associated Hilbert space of analytic functions on the unit disk developed by Kriete and Trutt. We also make a connection between the adjoint of the Cesàro operator and certain composition operators on H 2 which have universal translates in the sense of Rota.