Goffman C., Pedrick G. First Course in Functional Analysis

Prentice-Hall Inc., 1965. — 295 p.Portions of this book have been used by the authors in beginning graduate courses at Purdue University during the past several years.
Our view is that analysis itself is basic and that the abstract theories to which it leads are primarily of interest as tools which may be used in treating problems in analysis. This includes the theories of metric spaces, compactness and lower semicontinuity, normed vector spaces, Hilbert spaces, ordered vector spaces, Banach algebras, etc. Thus, we consider the abstract theories themselves only in part and then indicate their roles in analysis by giving various applications. In this regard, many important applications have not been considered because they are too complicated to be treated in an introductory study.