General Functional Analysis

Postgraduate course

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)

Recommended Previous Knowledge
MAT211 Real Analysis and MAT215 Theory of Measure and Integration
Compulsory Assignments and Attendance
Forms of Assessment
Oral examination
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.