The Backward Shift on the Hardy Space

Book excerpt: Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, "parts" of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction operators and potentially have connections to understanding the invariant subspaces of a general linear operator. This book is a thorough treatment of the characterization of the backward shift invariant subspaces of the well-known Hardy spaces H{p}. The characterization of the backward shift invariant subspaces of H{p} for 1