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Welcome to the C*-algebra course!

Our plan is to cover the following topics, roughly in this order:

• First examples of C*-algebras
• Commutative case
  • Gelfand transform and functional calculus
  • Gelfand-Naimark theorem
• Basic structure theory
  • Unitization Positive elements
  • Approximate units
  • Ideals and homomorphisms
  • Tensor products
• von Neumann algebras
  • Operator topologies; von Neumann algebras
  • von Neumann's double commutant theorem
  • Kaplansky's density theorem
• Representation theory of operator algebras
  • States; Gelfand-Naimark-Segal construction
  • Irreducible representations and pure states
  • Representations of algebras of compact operators; Voiculescu¡¯s theorem
...