Banach and Hilbert Spaces

Abstract

This chapter supplies the functional analytic material required for our study of existence of solutions of linear elliptic equations in Chapters 6 and 8. This material will be familiar to a reader already versed in basic functional analysis but we shall assume some acquaintance with elementary linear algebra and the theory of metric spaces. Unless otherwise indicated, all linear spaces used in this book are assumed to be defined over the real number field. The theory of this chapter, however, carries over almost unchanged if the real numbers are replaced by the complex numbers.