The Book
This book covers topics appropriate for a first-year graduate course preparing students for the doctorate degree. The first half of the book presents the core of measure theory, including an introduction to the Fourier transform. The second half of the book treats basic functional analysis. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and c*-algebras. lt concludes with a characterization of the unitary equivalence classes of normal operators on a Hilbert space. The book is self-contained and only relies on a background in functions of a single valuable and the elements of metric spaces. Following the author’s belief that the best way to learn is to start with the particular and proceed to the more general, it contains numerous examples and exercises.
The Author(s)
John B Conway is Professor Emeritus at George Washington University, Washington DC, USA.
Table of Contents
Preface
Chapter 1. Setting the Stage
Chapter 2. Elements of Measure Theory
Chapter 3. A Hilbert Space Interlude
Chapter 4. A Return to Measure Theory
Chapter 5. Linear Transformations
Chapter 6. Banach Spaces
Chapter 7. Locally Convex Spaces
Chapter 8. Duality
Chapter 9. Operators on a Banach Space
Chapter 10. Banach Algebras and Spectral Theory
Chapter 11. C*-Algebras d Elementary properties and examples
Appendix A.1. Baire Category Theorem
Appendix A.2. Nets 356
Bibliography
List of Symbols
Index