| 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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Book DetailsGraduate Studies in MathematicsVolume: 141; 2012; 367 ppMSC: 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.ReadershipUndergraduate and graduate students interested in analysis.
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Table of Contents
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Chapters
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Chapter 1. Setting the stage
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Chapter 2. Elements of measure theory
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Chapter 3. A Hilbert space interlude
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Chapter 4. A return to measure theory
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Chapter 5. Linear transformations
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Chapter 6. Banach spaces
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Chapter 7. Locally convex spaces
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Chapter 8. Duality
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Chapter 9. Operators on a Banach space
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Chapter 10. Banach algebras and spectral theory
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Chapter 11. C*-algebras
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Appendix
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Additional Material
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RequestsReview Copy – for reviewers who would like to review an AMS bookDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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
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Chapter 8. Duality
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Chapter 9. Operators on a Banach space
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Chapter 10. Banach algebras and spectral theory
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Chapter 11. C*-algebras
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Appendix
