NMAA07012U Introduction to Operator Algebras (IntroOpAlg)
Commutative Banach algebras, C*-algebras, commutative C*-algebras, continuous function calculus, states and representations, GNS representations, polar decomposition, non-unital C*-algebras and approximate units. von Neumann algebras. The bicommutant theorem and Kaplanski's density theorem. Borel function calculus. Type decomposition of von Neumann algebras.
The participants are expected to acquire the knowledge listed
above in the course description.
The participants are expected to be able to understand and apply the Gelfand transform and the GNS-construction, they must understand basic facts about order. They must have some familiarity with important examples of C*-algebras. They must understand the basics of von Neumann algebras.
The participants are expected to master the most fundamental concepts and constructions for C*-algebras and von Neumann algebras which are are used in further studies in operator algebras and in non-commutative geometry
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThere will be given 3 assignments, each of which will count equally towards the final grade.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
- 30 minutes oral examination with preparation times during which all aids are allowed. Several internal examiners.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
- Theory exercises