Self-Adjointness: Part 1. The Kato Inequality

Abstract

We will now concentrate on the class of self-adjoint operators in a Hilbert space 7i. Our first task will be to develop criteria that will allow us to determine which operators occurring in applications are self-adjoint. Then we will apply this to prove that Schrödinger operators with positive potentials are self-adjoint. After discussing in Chapters 11 and 12 the semiclassical analysis of eigenvalues for Schrödinger operators with positive, growing potentials, we will return to the question of self-adjointness in Chapter 13 and present the Kato-Rellich theory.