A Course in Abstract Analysis (Graduate Studies in Mathematics, Vol. 141) (Graduate Studies in Mathematics, 141)

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. This material can easily be covered in a semester. The second half of the book treats basic functional analysis and can also be covered in a semester. After the basics, it discusses linear transformations, duality, the elements of Banach algebras, and C*-algebras. It 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 variable 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. --Book cover 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 Appendix John B. Conway. Includes Bibliographical References And Index.