Hardcover ISBN:  9780821840986 
Product Code:  MMONO/233 
468 pp 
List Price:  $133.00 
MAA Member Price:  $119.70 
AMS Member Price:  $106.40 
Electronic ISBN:  9781470446550 
Product Code:  MMONO/233.E 
468 pp 
List Price:  $133.00 
MAA Member Price:  $119.70 
AMS Member Price:  $106.40 

Book DetailsTranslations of Mathematical MonographsVolume: 233; 2006MSC: Primary 46; 47;
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.ReadershipGraduate students and research mathematicians interested in functional analysis and operator theory.

Table of Contents

Chapters

Foundations: Categories and the like

Normed spaces and bounded operators (“Waiting for completeness”)

Banach spaces and their advantages

From compact spaces to Fredholm operators

Polynormed spaces, weak topologies, and generalized functions

At the gates of spectral theory

Hilbert adjoint operators and the spectral theorem

Fourier transform


Additional Material

Reviews

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 wellreadable 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


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

Chapters

Foundations: Categories and the like

Normed spaces and bounded operators (“Waiting for completeness”)

Banach spaces and their advantages

From compact spaces to Fredholm operators

Polynormed spaces, weak topologies, and generalized functions

At the gates of spectral theory

Hilbert adjoint operators and the spectral theorem

Fourier transform

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 wellreadable 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