Elementary Functional Analysis

Abstract

We assume that the reader already has knowledge of (complex) matrices, determinants, etc. In this chapter, we shall present basic machinery for dealing with vector spaces, especially Banach and Hilbert spaces. We do not go into depth in this direction as there are plenty of excellent specialised monographs available devoted to various aspects of the subject, see, e.g., [11, 35, 53, 59, 63, 70, 87, 89, 90, 116, 134, 146, 153]. However, we still make an independent presentation of a collection of results which are indispensable for anyone working in analysis, and which are useful for other parts of this book.