**Translations of Mathematical Monographs**

2006;
468 pp;
Hardcover

MSC: Primary 46; 47;

**Print ISBN: 978-0-8218-4098-6
Product Code: MMONO/233**

List Price: $133.00

AMS Member Price: $106.40

MAA Member Price: $119.70

**Electronic ISBN: 978-1-4704-4655-0
Product Code: MMONO/233.E**

List Price: $133.00

AMS Member Price: $106.40

MAA Member Price: $119.70

#### Supplemental Materials

# Lectures and Exercises on Functional Analysis

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*A. Ya. Helemskii*

The book is based on courses taught by the
author at Moscow State University. Compared to many other books on the
subject, it is unique in that the exposition is based on extensive use
of the language and elementary constructions of category theory. Among
topics featured in the book are the theory of Banach and Hilbert
tensor products, the theory of distributions and weak topologies, and
Borel operator calculus.

The book contains many examples illustrating the general theory
presented, as well as multiple exercises that help the reader to learn
the subject. It can be used as a textbook on selected topics of
functional analysis and operator theory. Prerequisites include linear
algebra, elements of real analysis, and elements of the theory of
metric spaces.

#### Readership

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

#### Reviews & Endorsements

The book contains many examples and exercises of different levels of difficulty. It requires only a basic knowledge of linear algebra, elements of real analysis, and metric spaces. It can be recommended to a broad spectrum of readers, to graduate students as well as young researchers.

-- European Mathematical Society Newsletter

The book is well-readable and written in a motivating way. Numerous examples and exercises illustrate the abstract theory and show its usefulness. Finally, this book is a true enrichment of the literature on functional analysis, especially because numerous proofs are very smart and fancy.

-- Zentralblatt MATH

(This) book is a pleasure to read. The author not only loves mathematics, but enjoys putting it into words. ...the next time I teach an introductory functional analysis course, it will be among the recommended texts.

-- Volker Runde for Mathematical Reviews

#### Table of Contents

# Table of Contents

## Lectures and Exercises on Functional Analysis

- Cover Cover11
- Title page iii4
- Dedication v6
- Contents vii8
- Preface xi12
- Foundations: Categories and the like 120
- Normed spaces and bounded operators (“Waiting for completeness”) 5574
- Banach spaces and their advantages 125144
- From compact spaces to Fredholm operators 191210
- Polynormed spaces, weak topologies, and generalized functions 245264
- At the gates of spectral theory 297316
- Hilbert adjoint operators and the spectral theorem 327346
- Fourier transform 413432
- Bibliography 455474
- Index 461480
- Back Cover Back Cover1490