Autumn 2009
MAT4360: C*-algebras

Recommended textbooks:
K.R. Davidson. C*-algebras by example.
G.J. Murphy. C*-algebras and operator theory.
G.K. Pedersen. C*-algebras and their automorphism groups.



Lecture 1 (18.08)
C*-algebras basics. Commutative C*-algebras. Functional calculus for normal elements.
Exercises.

Lecture 2 (25.08)
Positive elements. States and representations. Gelfand-Naimark theorem.
Exercises.

Lecture 3 (1.09)
Topologies on B(H). Von Neumann algebras. Tensor products.
Exercises.

Lecture 4 (21.09)
The von Neumann double commutant theorem.

Lecture 5 (30.09)
The Kaplanasky density theorem. Irreducible representations.
Exercises.

Lecture 6 (2.10)
Pure states. Algebras of compact operators.
Exercises.

Lecture 7 (14.10)
Approximate units. Ideals.
Exercises.

Lecture 8 (16.10)
Type I algebras. The Toeplitz algebra.
Exercises.

Lecture 9 (21.10)
Fredholm operators. Toeplitz operators.
Exercises.

Lecture 10 (28.10)
AF-algebras. Bratteli diagrams.

Lecture 11 (4.11)
Perturbation results.

Lecture 12 (11.11)
UHF-algebras. Ideals in AF-algebras.

Lecture 13 (18.11)
K-theory.

Lecture 14 (25.11)
K-theory for AF-algebras.