MENU

You are here

C* algebras

Lecturer: 
Course Type: 
PhD Course
Academic Year: 
2018-2019
Period: 
March - April
Duration: 
20 h
Description: 

Course contents
• Basic functional analysis, Banach spaces, linear operators
• Banach algebras, spectrum, Gelfand transform, (holomorphic) functional calculus
• C ∗ -algebras and their basic properties
• Gelfand-Naimark duality between C ∗ -algebras and locally compact Hausdorff spaces
• Continuous functional calculus, positive elements, approximate units
• Basics of von Neumann algebras
• (pure) states and (irreducible) representations
• Gelfand-Naimark-Segal (GNS) construction
Further possible topics (if time permits)
• multipliers
• tensor products
• group C ∗ -algebras, crossed products

Examination
The exam will consist of a seminar presentation on an advanced topic related to the
course.

Recommended literature
1. B. Blackadar, Operator algebras: Theory of C ∗ -algebras and von Neumann alge-
bras, Encyclopaedia of Mathematical Sciences, vol. 13, Springer, 2006.
2. J. Conway, A course in functional analysis Second edition. Graduate Texts in
Mathematics, 96. Springer-Verlag, New York, 1990.

Location: 
A-136
Next Lectures: 
Monday, March 25, 2019 - 11:00 to 13:00
Friday, March 29, 2019 - 11:00 to 13:00

Sign in