NMAA07012U  Introduction to Operator Algebras (IntroOpAlg)

Volume 2013/2014
Education
MSc Programme in Mathematics
Content
Commutative Banach algebras, C*-algebras, commutative C*-algebras, states and representations, GNS representations, polar decomposition, non-unital C*-algebras, approximate units and the multiplier algebra. Towards the end of the course we shall discuss selected examples of interesting C*-algebras such as the Toeplitz algebra, AF-algebras, irrational rotation C*-algebras, the Cuntz algebras, group C*-algebras
Learning Outcome
The participants are expected to acquire the knowledge listed above in the course description.

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.

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
Functional Analysis (FunktAn) and Analysis 2 (An2) or similar introductory courses on functional analysis and analysis
5 hours of lectures plus 3 hours of tutorials per week in 8 weeks (last assignment is due in week 9).
Credit
7,5 ECTS
Type of assessment
Continuous assessment
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
Re-exam
Oral examination. Several internal examiners
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

  • Category
  • Hours
  • Lectures
  • 40
  • Preparation
  • 122
  • Exam
  • 20
  • Theory exercises
  • 24
  • Total
  • 206