**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’ 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