Introduction to C*-algebras

Dr. Gherardo Piacitelli


  1. Definition of C*-algebra. Gelfand transform, functional calculus, representation theory. GNS construction. Universal representation. Geometry of states
  2. Operator algebras: Von Neumann Algebras. Weak topology, bicommutant theorem, classification of factors.
  3. Noncommutative integration. Tomita-Takesaki theory and applications to statistical mechanics. KMS states and applications.
  4. Tensor C* categories and application to superselection theory in local quantum physics.