During the last 15 or 20 years much progress has been made in the theory of non-self-adjoint operators on Hilbert and Banach spaces.
The present volume is intended to provide an introduction to the
subject.
The first four chapters are devoted to standard material on
linear functional analysis. However, whenever possible a unified
approach is used, and this is the case, for example, for the three
basic theorems of linear functional analysis which are treated
consequences of a unique theorem. Chapter 5 is concerned with the
general spectral representation of operators on Hilbert spaces and
depends on the Banach algebra theory developed in Chapter 4.