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A Course in Abstract Analysis
 
John B. Conway George Washington University, Washington, DC
A Course in Abstract Analysis
Hardcover ISBN:  978-0-8218-9083-7
Product Code:  GSM/141
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-0-8218-9160-5
Product Code:  GSM/141.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-9083-7
eBook: ISBN:  978-0-8218-9160-5
Product Code:  GSM/141.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
A Course in Abstract Analysis
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A Course in Abstract Analysis
John B. Conway George Washington University, Washington, DC
Hardcover ISBN:  978-0-8218-9083-7
Product Code:  GSM/141
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
eBook ISBN:  978-0-8218-9160-5
Product Code:  GSM/141.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-0-8218-9083-7
eBook ISBN:  978-0-8218-9160-5
Product Code:  GSM/141.B
List Price: $220.00 $177.50
MAA Member Price: $198.00 $159.75
AMS Member Price: $176.00 $142.00
  • 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.

    Readership

    Undergraduate and graduate students interested in analysis.

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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.

Readership

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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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