A Course in Abstract Analysis
John B Conway
Price
1700
ISBN
9781470425876
Language
English
Pages
384
Format
Paperback
Dimensions
180 x 240 mm
Year of Publishing
2016
Territorial Rights
Restricted
Imprint
Universities Press

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.

John B Conway is Professor Emeritus at George Washington University, Washington DC, USA.

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

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