Entry requirements

60 credits in mathematics. Real Analysis is recommended.

Learning outcomes

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

• use basic functional analytic formalism in normed spaces;
• use ON-systems and orthogonal projections in Hilbert spaces;
• solve simple problems about the weak topology;
• solve simple Hilbert space spectral theory problems.

Content

Topology in metric spaces. Normed spaces, Banach spaces, inner product spaces, Hilbert spaces. Linear operators. Dual space. Basic theorems in functional analysis: Hahn-Banach's theorem, Banach-Steinhaus' theorem. Strong and weak convergence. Convergence of sequences of operators. The spectral theory for compact symmetric operators.

Instruction

Lectures and exercises.

Assessment

Written examination at the end of 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.