An Introduction to Operators on the Hardy-Hilbert Space

For example, very elementary concepts from Hilbert space provide simple proofs of the Poisson integral (Theorem 1. The fundamental theorem about zeros of fu- tions in the Hardy–Hilbert space (Corollary 2. The Hardy–Hilbert space context is necessary to understand the structure of the invariant subspaces of the unilateral shift (Theorem 2.