This course counts as a core course in the Bachelor's degree programme in Mathematics. Holders of an ETH Zurich Bachelor's degree in Mathematics who didn't use credits from neither 401-3461-00L Functional Analysis I nor 401-3462-00L Functional Analysis II for their Bachelor's degree still can have recognised this course for the Master's degree. Furthermore, at most one of the three course units 401-3461-00L Functional Analysis I 401-3531-00L Differential Geometry I 401-3601-00L Probability Theory can be recognised for the Master's degree in Mathematics or Applied Mathematics.
Baire category; Banach and Hilbert spaces, bounded linear operators; three fundamental principles: Uniform boundedness, open mapping/closed graph theorem, Hahn-Banach; convexity; dual spaces; weak and weak* topologies; Banach-Alaoglu; reflexive spaces; compact operators and Fredholm theory; closed range theorem; spectral theory of self-adjoint operators in Hilbert spaces.
Lecture Notes on "Funktionalanalysis I" by Michael Struwe
Performance assessment information (valid until the course unit is held again)