Introduction to Operator Algebras (IntroOpAlg)
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. AF 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
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.
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Category
- Hours
- Lectures
- 40
- Preparation
- 112
- Theory exercises
- 24
- Exam
- 30
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAA07012U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 3
- Schedulegroup
-
A
- Capacity
- No limit
The number of seats may be reduced in the late registration period - Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Søren Eilers (6-686c6f687576437064776b316e7831676e)
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Courseinformation of students