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. Key examples of C*-algebras. Von Neumann algebras. The bicommutant theorem and Kaplansky's density theorem. Borel function calculus.
MSc Programme in Mathematics
MSc Programme in Mathematics with a minor subject
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.
5 hours of lectures plus 3 hours of tutorials per week in 8 weeks (last assignment is due in week 9).
Kehe Zhu: An introduction to operator algebras (or equivalent), along with handout notes.
Functional Analysis (FunkAn) and Lebesgueintegralet og målteori
(LIM) - alternatively Analyse 2 (An2) from previous years or
similar introductory courses on functional analysis and analysis
Academic qualifications equivalent to a BSc degree is recommended.
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
- Type of assessment details
- There 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.
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 3
- No limit
The number of seats may be reduced in the late registration period
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Søren Eilers (6-6d71746d7a7b4875697c7036737d366c73)
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Courseinformation of students