Table of Contents

Banach Algebras and Spectral Theory
Banach Algebras: Basic Concepts
Gelfand Theory
Nonunital Banach Algebras
The Spectral Theorem
Spectral Theory of *-Representations
Notes and References
Locally Compact Groups
Topological Groups
Haar Measure
Interlude: Some Technicalities
The Modular Function
Convolutions
Homogeneous Spaces
Notes and References
Basic Representation Theory
Unitary Representations
Representations of a Group and its Group Algebra
Functions of Positive Type
Notes and References
Analysis on Locally Compact Abelian Groups
The Dual Group
The Fourier Transform
The Pontrjagin Duality Theorem
Representations of Locally Compact Abelian Groups
Closed Ideals in L1(G)
Spectral Synthesis
The Bohr Compactification
Notes and References
Analysis on Compact Groups
Representations of Compact Groups
The Peter-Weyl Theorem
The Fourier Transform on Compact Groups
Examples
Notes and References
Induced Representations
The Inducing Construction
The Frobenius Reciprocity Theorem
Pseudomeasures and Induction in Stages
Systems of Imprimitivity
The Imprimitivity Theorem
Introduction to the Mackey Machine
Examples
Notes and References
Further Topics in Representation Theory
The Group C* Algebra
The Structure of the Dual Space
Tensor Products
Direct Integral Decompositions
The Plancherel Theorem
Examples
Appendix 1. Hilbert Space Miscellany
Appendix 2. Trace-Class and Hilbert-Schmidt Operators
Appendix 3. Vector-Valued Integrals
Bibliography
Index