Schedule, syllabus and examination date

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Course content

The course is a continuation of MAT4410 – Advanced Linear Analysis and presents functional analysis from a more advanced perspective. Topics covered are: an introduction to locally convex spaces (including the Hahn-Banach separation theorem, weak and weak*-topologies, Alaoglu's theorem, Krein-Milman's theorem); more on operators on Hilbert spaces (including polar decomposition, the spectral theorem for normal compact operators, index theory for Fredholm operators, trace class operators, Hilbert-Schmidt operators); the Gelfand theory for commutative Banach algebras and commutative C*-algebras with application to the spectral theory for normal operators; an introduction to the theory of unbounded operators on Hilbert spaces.

Learning outcome

The course combines ideas and methods from different areas of mathematics. It is designed especially for students who want to choose operator algebras as their speciality, but the content of the course will also be useful to students interested in other branches of analysis.


Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

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

Overlapping courses

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 


4 hours of lectures/exercises every week for the duration of the semester.

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.


1 mandatory assignment.

Final oral examination.

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 scale from A to F, where A is the best grade and F is a fail. 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






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


The same semester as taught.

Teaching language


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