This classic text is written for graduate courses in functional analysis. This text is used in modern investigations in analysis and applied mathematics. This new edition includes up-to-date presentations of topics as well as more examples and exercises. New topics include Kakutani's fixed point theorem, Lamonosov's invariant subspace theorem, and an ergodic theorem.
Preface
Part I : General Theory
Chapter 1 : Topological Vector Space
Chapter 2 : Completeness
Chapter 3 : Convexity
Chapter 4 : Duality in Banach Spaces
Chapter 5 : Some Applications
Part II : Distributions and Fourier Transforms
Chapter 6 : Test Functions and Distributions
Chapter 7 : Fourier Transforms
Chapter 8 : Applications to Differential Equations
Chapter 9 : Tauberian Theory
Part III : Banach Algebras and Spectral Theory
Chapter 10 : Banach Algebras
Chapter 11 : Commutative Banach Algebras
Chapter 12 : Bounded Operators on a Hillbert Space
Chapter 13 : Unbounded Operators
Appendix A : Compactness and Continuity
Appendix B : Notes and Comments
Bibliography
List of Special Symbols
Index
