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. 

Education

MSc Programme in Mathematics

MSc Programme in Mathematics with a minor subject

Learning outcome

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.

Written
Oral
Individual
Collective

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
  • Søren Eilers   (6-686c6f687576437064776b316e7831676e)
Saved on the 14-02-2024

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