A Course in Functional Analysis

John B. Conway (auth.)9783540960423, 9780387960425, 0387960422, 3540960422

This book is an introductory text in functional analysis, aimed at the graduate student with a firm background in integration and measure theory. Unlike many modern treatments, this book begins with the particular and works its way to the more general, helping the student to develop an intuitive feel for the subject. For example, the author introduces the concept of a Banach space only after having introduced Hilbert spaces, and discussing their properties. The student will also appreciate the large number of examples and exercises which have been included.

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Table of contents :
Front Matter….Pages i-xiv
Hilbert Spaces….Pages 1-25
Operators on Hilbert Space….Pages 26-64
Banach Spaces….Pages 65-101
Locally Convex Spaces….Pages 102-126
Weak Topologies….Pages 127-169
Linear Operators on a Banach Space….Pages 170-190
Banach Algebras and Spectral Theory for Operators on a Banach Space….Pages 191-236
C *-Algebras….Pages 237-260
Normal Operators on Hilbert Space….Pages 261-309
Unbounded Operators….Pages 310-352
Fredholm Theory….Pages 353-374
Back Matter….Pages 375-406