MAT4350 – Functional analysis
Course description
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 exciting 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.
Admission
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.
Prerequisites
Recommended previous knowledge
Knowledge corresponding to MAT3300 – Measure and integration (discontinued)/MAT4300 – Measure and integration (discontinued), MAT3500 – Topology/MAT4500 – Topology and MAT4340 – Elementary functional analysis (discontinued).
Overlapping courses
*The information about overlaps is not complete. Contact the Department for more information if necessary.
Teaching
4 hours lectures/exercises per week.
Examination
Oral exam. Letter grading (A-F).
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.