Schedule, syllabus and examination date

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Changes in the course due to coronavirus

Autumn 2020 the exams of most courses at the MN Faculty will be conducted as digital home exams or oral exams, using the normal grading scale. The semester page for your course will be updated with any changes in the form of examination.

See general guidelines for examination at the MN Faculty autumn 2020.

Course content

The course gives an introduction to C*-algebras and von Neumann algebras, which are the most important classes of operator algebras. Such algebras have fundamental applications in various areas of mathematics and in quantum physics. After having covered the basic results in the theory, some important classes of examples will be studied. The choice of examples may vary from one year to another, depending on the interests of the students following the course.

Learning outcome

After completing the course you:

  • are familiar with the definitions of C*-algebras and von Neumann algebras, and with basic related concepts, such as *-homomorphisms, ideals, quotients, approximate units and multiplier algebras;
  • know about the positive cone of a C*-algebra, how it induces an order on the self-adjoint elements and how it is used to define states;
  • know how to construct the GNS-representation associated with a state and how to represent a C*-algebra faithfully as bounded operators on a Hilbert space;
  • know the connection between pure states and irreducible representations of a C*-algebra;
  • have a good understanding of several operator topologies and know how to characterize von Neumann algebras with the help of double commutants;
  • can describe C*-algebras of compact operators and have a knowledge of other important classes of C*-algebras.

Admission to the course

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.

MAT4450 – Advanced Functional Analysis

Overlapping courses


4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.


Final oral exam which counts 100 % towards the final grade.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses:MAT9460 – C*-algebras

Examination support material

No examination support material is allowed.

Language of examination

Courses 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 scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Dec. 1, 2020 2:20:59 PM

Facts about this course


Taught according to demand and resources. Contact if you are interested in this course.

Autumn semester 2020: This course will only be given as a self-study course for master students at the Department of Mathematics.

Teaching language