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Introduction to C*-algebras

Lecturer: 
Koen van den Dungen
Course Type: 
PhD Course
Academic Year: 
2017-2018
Period: 
Oct - Nov
Duration: 
20 h
Description: 
This course provides a brief introduction to C*-algebras. The course will cover at least the following topics:
- brief recap on Banach spaces and linear operators;
- Banach algebras: spectrum, Gelfand transform, Stone-Weierstrass theorem;
- C*-algebras: definition and basic properties;
- Gelfand-Naimark duality between commutative C*-algebras and locally compact Hausdorff spaces;
- continuous functional calculus;
- positive elements, approximate units;
- von Neumann algebras: definition and basic properties;
- (pure) states and (irreducible) representations;
- GNS (Gelfand-Naimark-Segal) construction.
Additional Material: 
Location: 
A-136

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