Course topics

  1. Background material in functional analysis and Hilbert space theory; basics of Banach algebras, and Gelfand theory.
  2. Basic results: commutative $C^*$-algebras, positivity, ideals and quotients, states and representations, the GNS constuction, the algebra of compact operators.
  3. A discussion of some basic examples in the theory (e.g. AF algebras, Toeplitz and Cuntz algebras, irrational rotation algebras, as time permits). Introduction to K-theory.

Further topics as time permits.

Course Information

University course catalogue:
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