MAT4450 – Advanced Functional Analysis
Schedule, syllabus and examination date
Changes in the course due to coronavirus
Autumn 2020 we plan for teaching and examinations to be conducted as described in the course description and on semester pages. However, changes may occur due to the corona situation. You will receive notifications about any changes at the semester page and/or in Canvas.
Spring 2020: Teaching and examinations was digitilized. See changes and common guidelines for exams at the MN faculty spring 2020.
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.
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 at UiO register for courses and exams in Studentweb.
Recommended previous knowledge
- 7 credits overlap with MAT4350 – Functional analysis (discontinued).
- 3 credits overlap with MAT4340 – Elementary functional analysis (discontinued).
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 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.
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: