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Principles of Functional Analysis: Second Edition
Martin Schechter, University of California, Irvine, CA
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Graduate Studies in Mathematics
2002; 425 pp; hardcover
Volume: 36
ISBN-10: 0-8218-2895-9
ISBN-13: 978-0-8218-2895-3
List Price: US$68
Member Price: US$54.40
Order Code: GSM/36
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Functional analysis plays a crucial role in the applied sciences as well as in mathematics. It is a beautiful subject that can be motivated and studied for its own sake. In keeping with this basic philosophy, the author has made this introductory text accessible to a wide spectrum of students, including beginning-level graduates and advanced undergraduates.

The exposition is inviting, following threads of ideas, describing each as fully as possible, before moving on to a new topic. Supporting material is introduced as appropriate, and only to the degree needed. Some topics are treated more than once, according to the different contexts in which they arise.

The prerequisites are minimal, requiring little more than advanced calculus and no measure theory. The text focuses on normed vector spaces and their important examples, Banach spaces and Hilbert spaces. The author also includes topics not usually found in texts on the subject.

This Second Edition incorporates many new developments while not overshadowing the book's original flavor. Areas in the book that demonstrate its unique character have been strengthened. In particular, new material concerning Fredholm and semi-Fredholm operators is introduced, requiring minimal effort as the necessary machinery was already in place. Several new topics are presented, but relate to only those concepts and methods emanating from other parts of the book. These topics include perturbation classes, measures of noncompactness, strictly singular operators, and operator constants.

Overall, the presentation has been refined, clarified, and simplified, and many new problems have been added.

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Readership

Advanced undergraduates, graduate students, and pure and applied research mathematicians interested in functional analysis and operator theory.

Reviews

"This excellent book provides an elegant introduction to functional analysis ... carefully selected problems ... This is a nicely written book of great value for stimulating active work by students. It can be strongly recommended as an undergraduate or graduate text, or as a comprehensive book for self-study."

-- European Mathematical Society Newsletter

From a review of the first edition:

"`Charming' is a word that seldom comes to the mind of a science reviewer, but if he is charmed by a treatise, why not say so? I am charmed by this book.

"Professor Schechter has written an elegant introduction to functional analysis including related parts of the theory of integral equations. It is easy to read and is full of important applications. He presupposes very little background beyond advanced calculus; in particular, the treatment is not burdened by topological `refinements' which nowadays have a tendency of dominating the picture.

"The book can be warmly recommended to any reader who wants to learn about this subject without being deterred by less relevant introductory matter or scared away by heavy prerequisites."

-- American Scientist

"This is an excellent book e.g. for somebody working in applied mathematics who wants to learn operator theory from scratch. It contains a wealth of material ... presented in a very elegant way ... book is very pleasant to read."

-- Zentralblatt MATH

Table of Contents

  • Basic notions
  • Duality
  • Linear operators
  • The Riesz theory for compact operators
  • Fredholm operators
  • Spectral theory
  • Unbounded operators
  • Reflexive Banach spaces
  • Banach algebras
  • Semigroups
  • Hilbert space
  • Bilinear forms
  • Selfadjoint operators
  • Measures of operators
  • Examples and applications
  • Glossary
  • Major Theorems
  • Bibliography
  • Index
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