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Bibliographic Details

Title: Introduction to Functional Analysis (Oxford Graduate Texts in Mathematics)
Publisher: Clarendon Press
Publication Date: 1997
Language: English
ISBN 10: 0198514859
ISBN 13: 9780198514855
Binding: Hardcover
Condition: good

About this title

Synopsis

The book is written for students of mathematics and physics who have a basic knowledge of analysis and linear algebra. It can be used as a textbook for courses and/or seminars in functional analysis. Starting from metric spaces it proceeds quickly to the central results of the field, including the theorem of HahnBanach. The spaces (p Lp (X,(), C(X)' and Sobolov spaces are introduced. A chapter on spectral theory contains the Riesz theory of compact operators, basic facts on Banach and C*-algebras and the spectral representation for bounded normal and unbounded self-adjoint operators in Hilbert spaces. An introduction to locally convex spaces and their duality theory provides the basis for a comprehensive treatment of Fr�chet spaces and their duals. In particular recent results on sequences spaces, linear topological invariants and short exact sequences of Fr�chet spaces and the splitting of such sequences are presented. These results are not contained in any other book in this field.

Review

The book can be warmly recommended to graduate students of mathematics and physics and also everybody interested in functional analysis.

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