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A Course in Abstract Analysis

John B. Conway George Washington University, Washington, DC
Available Formats:
Hardcover ISBN: 978-0-8218-9083-7
Product Code: GSM/141
List Price: $80.00 MAA Member Price:$72.00
AMS Member Price: $64.00 Electronic ISBN: 978-0-8218-9160-5 Product Code: GSM/141.E List Price:$75.00
MAA Member Price: $67.50 AMS Member Price:$60.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $120.00 MAA Member Price:$108.00
AMS Member Price: $96.00 Click above image for expanded view A Course in Abstract Analysis John B. Conway George Washington University, Washington, DC Available Formats:  Hardcover ISBN: 978-0-8218-9083-7 Product Code: GSM/141  List Price:$80.00 MAA Member Price: $72.00 AMS Member Price:$64.00
 Electronic ISBN: 978-0-8218-9160-5 Product Code: GSM/141.E
 List Price: $75.00 MAA Member Price:$67.50 AMS Member Price: $60.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$120.00 MAA Member Price: $108.00 AMS Member Price:$96.00
• Book Details

Graduate Studies in Mathematics
Volume: 1412012; 367 pp
MSC: Primary 28; 46;

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.

Undergraduate and graduate students interested in analysis.

• Chapters
• 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

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Volume: 1412012; 367 pp
MSC: Primary 28; 46;

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.

Undergraduate and graduate students interested in analysis.

• Chapters
• 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
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