Ebook: Elementary functional analysis

This text is intended for a one-semester introductory course in functional analysis for graduate students and well-prepared advanced undergraduates in mathematics and related fields. It is also suitable for self-study, and could be used for an independent reading course for undergraduates preparing to start graduate school.

While this book is relatively short, the author has not sacrificed detail. Arguments are presented in full, and many examples are discussed, making the book ideal for the reader who may be learning the material on his or her own, without the benefit of a formal course or instructor. Each chapter concludes with an extensive collection of exercises.

The choice of topics presented represents not only the author's preferences, but also her desire to start with the basics and still travel a lively path through some significant parts of modern functional analysis. The text includes some historical commentary, reflecting the author's belief that some understanding of the historical context of the development of any field in mathematics both deepens and enlivens one's appreciation of the subject.

The prerequisites for this book include undergraduate courses in real analysis and linear algebra, and some acquaintance with the basic notions of point set topology. An Appendix provides an expository discussion of the more advanced real analysis prerequisites, which play a role primarily in later sections of the book.

Barbara MacCluer is Professor of Mathematics at University of Virginia. She also co-authored a book with Carl Cowen, Composition Operators on Spaces of Analytic Functions (CRC 1995).

This nicely written manuscript takes a gentler approach than other functional analysis graduate texts, and includes an improved approach along with a better choice of topics. The concise treatment makes this ideal for a one-semester course. The exercises in this manuscript are numerous and of a very high quality. Interesting historical tidbits are scattered throughout the text, many of which will be new to most readers. The main prerequisites are basic undergraduate courses in real analysis, linear algebra, and point set topology.