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 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
-
Oral exam on basis of previous submission, 25 min
- Type of assessment details
- 25 min oral examination with 25 min preparation time
The students must hand in two written assignments to able to participate in the oral exam. The grade will be based on the latter.
The written assignments must be handed in and approved no later than two weeks prior to the oral examination.
The oral exam will in part be about the two written assignments. In part based on course curriculum - Aid
- Only certain aids allowed (see description below)
For the written assignments all aids are allowed.For the oral exam no aids allowed.
For the preparation time all written aids are allowed.
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
Internal examiner(s)
- Re-exam
-
Same as the ordinary exam.
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 (6-7875786a67734673677a6e34717b346a71)
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Kursusinformation for indskrevne studerende