Entry requirements

120 credits including 90 credits in mathematics. Linear Algebra II. Participation in Real Analysis. Proficiency in English equivalent to the Swedish upper secondary course English 6.

Learning outcomes

On completion of the course, the student should be able to:

• give an account of basic properties of Banach spaces and Hilbert spaces;
• give an account of basic properties of operators on Banach spaces and Hilbert spaces;
• formulate and apply central theorems in functional analysis, and to be able to give an account of their proofs;
• use the theory, methods and techniques of the course to solve problems.

Content

Topology in metric spaces. Normed spaces. Banach spaces, inner product spaces, Hilbert spaces. Linear operators. Basic functional analytic theorems: Hahn-Banach's theorem, Banach-Steinhaus' theorem, the open mapping and the closed graph theorems. Strong and weak convergence. Convergence of sequences of operators. Spectral theory. The spectral theorem for compact self-adjoint operators.

Instruction

Lectures and problem solving sessions.

Assessment

Oral examination at the end of the course combined with assignments given during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course cannot be included in the same degree as Functional Analysis, Introductory Course (1MA321), Functional Analysis (1MA218).