Chapter 10 - Unbounded Operators

Abstract

In this chapter the focus is on unbounded linear operators, especially differential operators. The notions of closed and closeable linear operator are presented, and illustrated with examples. The concept of adjoint operator is generalized to a suitable class of unbounded linear operators on a Hilbert space, and the significance of the adjoint operator for solvability of linear operator equations reexamined in this context. The existence of self-adjoint extensions of symmetric operators is also discussed.