**Graduate Studies in Mathematics**

Volume: 36;
2002;
425 pp;
Hardcover

MSC: Primary 46; 47;

Print ISBN: 978-0-8218-2895-3

Product Code: GSM/36

List Price: $72.00

Individual Member Price: $57.60

**Electronic ISBN: 978-1-4704-1147-3
Product Code: GSM/36.E**

List Price: $72.00

Individual Member Price: $57.60

# Principles of Functional Analysis: Second Edition

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*Martin Schechter*

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.

#### Table of Contents

# Table of Contents

## Principles of Functional Analysis: Second Edition

- Cover Cover11 free
- Other titles in this series i2 free
- Title page v6 free
- Contents ix10 free
- Preface to the revised edition xv16 free
- From the preface to the first edition xix20 free
- Basic notions 124 free
- Duality 2952
- Linear operators 5578
- The Riesz theory for compact operators 77100
- Fredholm operators 101124
- Spectral theory 129152
- Unbounded operators 155178
- Reflexive Banach spaces 183206
- Banach algebras 201224
- Semigroups 225248
- Hilbert space 243266
- Bilinear forms 265288
- Selfadjoint operators 297320
- Measures of operators 325348
- Examples and applications 359382
- Glossary 393416
- Major Theorems 405428
- Bibliography 419442
- Index 423446 free
- Back Cover Back Cover1450

#### 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

‘Charming&rsquo 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