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. 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
- Category
- Hours
- Exam
- 30
- Lectures
- 40
- Preparation
- 112
- Theory exercises
- 24
- Total
- 206
As
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- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessmentThere will be given 3 assignments, each of which will count equally towards the final grade.
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner.
- Re-exam
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.
Course information
- Language
- English
- Course code
- NMAA07012U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- A
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Mikael Rørdam (6-7976796b68744774687b6f35727c356b72)