This course is discontinued

Course content

The course is a continuation of MAT4340 – Elementary functional analysis (discontinued). Functional analysis is now developed in a broader perspective by using concepts from topology and measure- and integration-theory. Central themes are Banach spaces and their dual spaces, the fundamental theorems
(e.g. the Hahn-Banach theroem, the open mapping theorem, the closed graph theorem, the Banach-Steinhaus theorem, Alaoglu's theorem), the Gelfand theory for commutative Banach algebras and commutative C*-algebras with applications to spectral theory. An introduction to the theory of unbounded operators on Hilbert spaces is also given.

Learning outcome

The course combines in an exiting way 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 all students interested in other branches of analysis.


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.

Overlapping courses

10 credits with MAT4350 – Functional analysis (discontinued).

*The information about overlaps is not complete. Contact the Department for more information if necessary.


4 hours lectures/exercises per week.


Oral exam.

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 due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.

Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.

Information about deferred and new examination (also called repeat examination) is found here

More information about examination at the Faculty of Mathematics and Natural Sciences can be found here

Facts about this course






Spring 2009

This version of the course was held for the last time Spring 2009. MAT4350 – Functional analysis (discontinued) will still be held.


Spring 2009

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.