A Beurling Theorem for almost-invariant subspaces of the shift operator

Abstract

A complete characterization of nearly-invariant subspaces of finite defect for the backward shift operator acting on the Hardy space is provided in the spirit of Hitt and Sarason's theorem. As a corollary we describe the almost-invariant subspaces for the shift and its adjoint.

11 pages. Revised version. To appear in J. Operator Theory