Preface

1 Fundamentals
1．1 What is Functional Analysis?
1．2 Normed Linear Spaces
1．3 Finite-Dimensional Spaces
1．4 Linear Operators
1．5 The Baire Category Theorem
1．6 The Three Big Results
1．7 Applications of the Big Three

2 Ode to the Dual Space
2．1 Introduction
2．2 Consequences of the Hahn-Banach Theorem

3 Hilbert Space
3．1 Introduction
3．2 The Geometry of Hilbert Space

4 The Algebra of Operators
4．1 Preliminaries
4．2 The Algebra of Bounded Linear Operators
4．3 Compact Operators

5 Banach Algebra Basics
5．1 Introduction to Banach Algebras
5．2 The Structure of a Banach Algebra
5．3 Ideals
5．4 The Wiener Tauberian Theorem

6 Topological Vector Spaces
6．1 Basic Ideas
6．2 Frechet Spaces

7 Distributions
7．1 Preliminary Remarks
7．2 Whatis a Distribution?
7．3 Operations on Distributions
7．4 Approximation of Distributions
7．5 The Fourier Transform

8 Spectral Theory
8．1 Background
8．2 The Main Result

9 Convexity
9．1 Introductory Thoughts
9．2 Separation Theorems
9．3 The Main Result

10 Fixed-Point Theorems
10．1 Banach's Theorem
10．2 Two Applications
10．3 The Schauder Theorem

Table of Notation
Glossary
Bibliography
Index
About the Author