General Functional Analysis
Postgraduate course
- ECTS credits
- 10
- Teaching semesters Autumn, Spring
- Course code
- MAT311
- Number of semesters
- 1
- Teaching language
- English
- Resources
- Schedule
Course description
Objectives and Content
Topics are general topology, Bancah spaces, Hahn Banach theorem, Baire categories with applications, weak convergence, Krein Milman theorem. Also applications of this to Lp spaces.
Learning Outcomes
After completing the course, students should be able to:
- Discuss concepts and definitions related to topological spaces.
- Present the main ideas of the proof of Tychonoff's theorem.
- Provide examples of results about Banach spaces related to Baire's theorem.
- State the Hahn–Banach theorem and explain its proof and applications.
- Describe various topologies on linear spaces and relate these to questions of convergence and compactness.
- Present fundamental theory and results about Hilbert spaces, such as the parallelogram law, orthonormal bases, projections, and bounded linear operators.
Semester of Instruction
Irregular, course will be offered if it is on this course list: Workbook: Emneliste for innreisende utvekslingsstudenter (uhad.no)