Introduces the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators and spectral theory of self-adjoint operators. This work presents the theorems and methods of abstract functional analysis and applications of these methods to Banach algebras and theory of unbounded self-adjoint operators. Series: Graduate Studies in Mathematics. Num Pages: 322 pages, Illustrations. BIC Classification: PBKF. Category: (P) Professional & Vocational. Dimension: 260 x 184 x 22. Weight in Grams: 750. . 2004. Hardcover. . . . . Books ship from the US and Ireland.

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Bibliographic Details

Title: Functional Analysis: An Introduction (Graduate Studies in Mathematics)
Publisher: American Mathematical Society
Publication Date: 2004
Language: English
ISBN 10: 0821836463
ISBN 13: 9780821836460
Binding: Hardcover
Condition: New

About this title

Synopsis

This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators.

The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book.

The text is ideal for a one-year course. It will also provide a sound basis for further study. It is suitable for graduate students and researchers interested in operator theory and functional analysis.

Review

This book contains a wealth of material. Each chapter concludes with a comprehensive set of exercises that serve to illustrate the theory. Solutions to the exercises are given in the final section. --Mathematical Reviews

This is a gentle introduction to functional analysis that is clearly written and comes with detailed, elegant and effective proofs and well-chosen examples. ... This book is written with great care and with much sympathy to the reader. It is pleasant to read... It is simply a good book to learn the foundations of functional analysis. --Zentralblatt MATH

Each chapter includes exercises, in total 195 of the them, all provided with solutions at the end of the book. The text is as self-contained as possible... The authors have taken special care to be brief and not to overload the students with the enormous amount of information available on the subject. --EMS Newsletter

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