NMAA07012U  Introduction to Operator Algebras (IntroOpAlg)

Volume 2017/2018
Education

MSc Programme in Mathematics

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. 

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.

 

Functional Analysis (FunkAn) 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
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 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
  • 112
  • Exam
  • 30
  • Theory exercises
  • 24
  • Total
  • 206