Course content

The Hahn-Banach theorem, the open mapping and closed graph theorems, the Banach-Steinhaus theorem, dual spaces, weak convergence, the Banach-Alaoglu theorem, and the spectral theorem for bounded self-adjoint operators.

Learning outcome

1. Knowledge. The student has knowledge of central concepts from functional analysis, including the Hahn-Banach theorem, the open mapping and closed graph theorems, the Banach-Steinhaus theorem, dual spaces, weak convergence, the Banach-Alaoglu theorem, and the spectral theorem for bounded self-adjoint operators.

2. Skills. The student is able to apply his or her knowledge of functional analysis to solve mathematical problems.

Learning methods and activities

Lectures, exercises and an oral final examination. The lectures will be given in English if they are attended by students from the Master's Programme in Mathematics for International students.

Recommended previous knowledge

TMA4145 Linear Methods and TMA4225 Foundation of Analysis.

Course materials

To be announced at the beginning of the term.

Credit reductions