MAT4450 – Advanced Functional Analysis

Schedule, syllabus and examination date

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Teaching and exams spring 2022

In light of the most recent infection control regulations, we will at the start of the spring semester 2022 increase our online teaching, while we at the same time try to maintain in-person teaching where this is possible. We hope to go back to more in-person teaching later on in the semester. You will be informed about any changes in teaching or examinations on the semester page, in Canvas or through your regular channels.

Read more about postponed exams for the autumn semester 2021.

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.

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.

Knowledge corresponding to MAT3400 – Linear Analysis with Applications/MAT4400 – Linear Analysis with Applications, MAT4410 – Advanced Linear Analysis and MAT3500 – Topology/MAT4500 – Topology.

Overlapping courses


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

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) Jan. 20, 2022 6:21:10 PM

Facts about this course


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

Teaching language