Operator Algebras
Course content
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
Knowledge:
The participants are expected to acquire the knowledge listed above
in the course description with an emphasis on
function calculus.
Skills:
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.
Competences:
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.
Advanced Vector Spaces (AdVec).
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.
- ECTS
- 7,5 ECTS
- Type of assessment
-
Continuous assessment
- Type of assessment details
- There 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 assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Category
- Hours
- Lectures
- 40
- Preparation
- 112
- Theory exercises
- 24
- Exam
- 30
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK23012U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 3
- Schedulegroup
-
A
- Capacity
- No limitation – unless you register in the late-registration period (BSc and MSc) or as a credit or single subject student.
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Mikael Rørdam (6-777477696672457266796d33707a336970)
Se skema
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Kursusinformation for indskrevne studerende