Lectures and Exercises on Functional AnalysisShare this page
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.
Table of Contents
Table of Contents
Lectures and Exercises on Functional Analysis
Graduate students and research mathematicians interested in functional analysis and operator theory.
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