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Functional Analysis: An Introduction
Yuli Eidelman and Vitali Milman, Tel Aviv University, Israel, and Antonis Tsolomitis, University of the Aegean, Samos, Greece

Graduate Studies in Mathematics
2004; 322 pp; hardcover
Volume: 66
ISBN-10: 0-8218-3646-3
ISBN-13: 978-0-8218-3646-0
List Price: US$65
Member Price: US$52
Order Code: GSM/66
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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 self-adjoint 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 self-adjoint operators.

The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. 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 one-year 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.

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Graduate students and research mathematicians interested in operator theory and functional analysis.


"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 well-chosen 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 self-contained 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

Table of Contents

Hilbert spaces and basic operator theory
  • Linear spaces; normed spaces; first examples
  • Hilbert spaces
  • The dual space
  • Bounded linear operators
  • Spectrum. Fredholm theory of compact operators
  • Self-adjoint operators
  • Functions of operators; spectral decomposition
Basics of functional analysis
  • Spectral theory of unitary operators
  • The fundamental theorems and the basic methods
  • Banach algebras
  • Unbounded self-adjoint and symmetric operators in \(H\)
  • Solutions to exercises
  • Bibliography
  • Symbols index
  • Subject index
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