Introduction to the theory of operators in Banach spaces

Abstract

This chapter is again preliminary; we present an outline of those parts of operator theory in Banach spaces which are needed in the perturbation theory developed in later chapters. The material is quite elementary, but the presentation is fairly complete, reference being made occasionally to the first chapter, so that this chapter can be read without previous knowledge of Banach space theory. It is also intended to be useful as an introduction to operator theory. To keep the chapter within reasonable length, however, some basic theorems (for example, the Baire category theorem and the Hahn-Banach extension theorem) are stated without proof¹.