Preface
Chapter 1. Introduction to C*-Algebras
1. Definition and examples
2. Abelian C*-algebras and the Functional Calculus
3. The positive elements in a C*-algebra
4. Approximate identities
5. Ideals in a C*-algebra
6. Representations of a C*-algebra
7. Positive linear functionals and the GNS construction
Chapter 2. Normal Operators
8. Some topologies on B(H)
9. Spectral measures
10. The Spectral Theorem
11. Star-cyclic normal operators
12. The commutant
13. Von Neumann algebras
14. Abelian von Neumann algebras
15. The functional calculus for normal operators
Chapter 3. Compact Operators
16. C*-algebras of compact operators
17. Ideals of operators
18. Trace class and Hilbert-Schmidt operators
19. The dual spaces of the compact operators and the trace class
20. The weak-star topology
21. Inflation and the topologies
Chapter 4. Some Non-Normal Operators
22. Algebras and lattices
23. Isometries
24. Unilateral and bilateral shifts
25. Some results on Hardy spaces
26. The functional calculus for the unilateral shift
27. Weighted shifts
28. The Volterra operator
29. Bergman operators
30. Subnormal operators
31. Essentially normal operators
Chapter 5. More on C*-Algebras
32. Irreducible representations
33. Positive maps
34. Completely positive maps
35. An application: Spectral sets and the Sz.-Nagy DilationTheorem
36. Quasicentral approximate identitites
Chapter 6. Compact Perturbations
37. Behavior of the spectrum under a compact perturbation
38. Bp perturbations of hermitian operators
39. The Weyl-von Neumann-Berg Theorem
40. Voiculescu's Theorem
41. Approximately equivalent representations
42. Some applications
Chapter 7. Introduction to Von Neumann Algebras
