NMAA07012U Introduction to Operator Algebras (IntroOpAlg)
MSc Programme in Mathematics
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. AF algebras. Von Neumann algebras. The bicommutant theorem and Kaplansky's density theorem. Borel function calculus.
The participants are expected to acquire the knowledge listed above in the course description with an emphasis on function calculus.
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 which are are used in further studies in operator algebras and in non-commutative geometry.
Kehe Zhu: An introduction to operator algebras (or equivalent), along with handout notes.
Academic qualifications equivalent to a BSc degree is recommended.
- Theory exercises
Individual written feedback on mandatory exercises. Individual or collective feedback on solutions presented by students at the exercise sessions.
- 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 30 min. preparation time 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.