This course is replaced by MAT9460 – C*-algebras.

Schedule, syllabus and examination date

Choose semester

Course content

The subject is a continuation of MAT4450 – Advanced Functional Analysis and the course gives an introduction to the theory of C*-algebras (often called operator algebras). The subject of C*-algebras may be viewed as a branch of functional analysis where particular non-commutative algebras are considered. The main part of the course will cover some of the fundamental results in the theory, including the Gelfand-Naimark representation theorem for C*-algebras, von Neumann`s double commutant theorem and Kaplansky`s density theorem. The examples presented and the additional content of the course will vary somewhat depending on the interests of the students.

Learning outcome

The course is primarily aimed at students who want to write a master thesis about operator algebras, but it may also be useful for other master students and doctoral students.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.


Recommended previous knowledge

MAT4450 – Advanced Functional Analysis.

Overlapping courses

10 credits overlap with MAT4360 – C*-algebras (continued)

For information about the potential partial overlap with other courses, contact the Department.


4 hours of lectures/exercises per week.

If few students apply for the course, it may be given as self-tuition with one hour of common academic supervision each week.


Oral exam.

In addition, each phd student is expected to give a one hour oral presentation on a topic of relevance (chosen in cooperation with the lecturer). The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Autumn 2017

Autumn 2016

Autumn 2014

Autumn 2011

Autumn. Taught according to demand and resources. If you want to attend the course, please send an e-mail to


Autumn 2017

Autumn 2016

Autumn 2014

Autumn 2011

According to demand and resources.

Teaching language


The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.