Hardcover ISBN:  9780821890837 
Product Code:  GSM/141 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9780821891605 
Product Code:  GSM/141.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821890837 
eBook: ISBN:  9780821891605 
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 
Hardcover ISBN:  9780821890837 
Product Code:  GSM/141 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9780821891605 
Product Code:  GSM/141.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Hardcover ISBN:  9780821890837 
eBook ISBN:  9780821891605 
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 DetailsGraduate Studies in MathematicsVolume: 141; 2012; 367 ppMSC: Primary 28; 46
This book covers topics appropriate for a firstyear 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 selfcontained 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.

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


Additional Material

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This book covers topics appropriate for a firstyear 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 selfcontained 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