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Hardcover ISBN:  9780821836460 
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eBook ISBN:  9781470411503 
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eBook ISBN:  9781470411503 
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Book DetailsGraduate Studies in MathematicsVolume: 66; 2004; 322 ppMSC: Primary 46; 47
This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of selfadjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded selfadjoint operators.
The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially selfcontained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book.
The text is ideal for a oneyear course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis.
ReadershipGraduate students and research mathematicians interested in operator theory and functional analysis.

Table of Contents

Part I. Hilbert spaces and basic operator theory

Chapter 1. Linear spaces; normed spaces; first examples

Chapter 2. Hilbert spaces

Chapter 3. The dual space

Chapter 4. Bounded linear operators

Chapter 5. Spectrum. Fredholm theory of compact operators

Chapter 6. Selfadjoint operators

Chapter 7. Functions of operators; spectral decomposition

Part II. Basics of functional analysis

Chapter 8. Spectral theory of unitary operators

Chapter 9. The fundamental theorems and the basic methods

Chapter 10. Banach algebras

Chapter 11. Unbounded selfadjoint and symmetric operators in $H$

Appendix. Solutions to exercises


Additional Material

Reviews

This book contains a wealth of material. Each chapter concludes with a comprehensive set of exercises that serve to illustrate the theory. Solutions to the exercises are given in the final section.
Mathematical Reviews 
This is a gentle introduction to functional analysis that is clearly written and comes with detailed, elegant and effective proofs and wellchosen examples. ... This book is written with great care and with much sympathy to the reader. It is pleasant to read... It is simply a good book to learn the foundations of functional analysis.
Zentralblatt MATH 
Each chapter includes exercises, in total 195 of the them, all provided with solutions at the end of the book. The text is as selfcontained as possible... The authors have taken special care to be brief and not to overload the students with the enormous amount of information available on the subject.
EMS Newsletter


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This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of selfadjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded selfadjoint operators.
The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially selfcontained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book.
The text is ideal for a oneyear course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis.
Graduate students and research mathematicians interested in operator theory and functional analysis.

Part I. Hilbert spaces and basic operator theory

Chapter 1. Linear spaces; normed spaces; first examples

Chapter 2. Hilbert spaces

Chapter 3. The dual space

Chapter 4. Bounded linear operators

Chapter 5. Spectrum. Fredholm theory of compact operators

Chapter 6. Selfadjoint operators

Chapter 7. Functions of operators; spectral decomposition

Part II. Basics of functional analysis

Chapter 8. Spectral theory of unitary operators

Chapter 9. The fundamental theorems and the basic methods

Chapter 10. Banach algebras

Chapter 11. Unbounded selfadjoint and symmetric operators in $H$

Appendix. Solutions to exercises

This book contains a wealth of material. Each chapter concludes with a comprehensive set of exercises that serve to illustrate the theory. Solutions to the exercises are given in the final section.
Mathematical Reviews 
This is a gentle introduction to functional analysis that is clearly written and comes with detailed, elegant and effective proofs and wellchosen examples. ... This book is written with great care and with much sympathy to the reader. It is pleasant to read... It is simply a good book to learn the foundations of functional analysis.
Zentralblatt MATH 
Each chapter includes exercises, in total 195 of the them, all provided with solutions at the end of the book. The text is as selfcontained as possible... The authors have taken special care to be brief and not to overload the students with the enormous amount of information available on the subject.
EMS Newsletter