Lectures and Exercises on Functional Analysis

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American Mathematical Soc. - Mathematics - 468 pages
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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.
 

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Contents

Categories and the Like
1
Normed Spaces and Bounded Operators
55
Banach Spaces and Their Advantages
125
From Compact Spaces to Fredholm Operators
191
Polynormed Spaces Weak Topologies and Generalized
245
functions
288
At the Gates of Spectral Theory
297
Hilbert Adjoint Operators and the Spectral Theorem
327
Fourier Transform
413
Bibliography
455
Index
461
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Page 6 - An order is said to be linear if for every x, y 6 X either x -< y, or y -< x. A set with a linear order is called a linearly ordered set.
Page 3 - The set of all mappings from a set X to a set Y is denoted by Map(X, Y).

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