This course is in many ways a continuation of the course TMA4145 Linear Methods. The main subjects are Banach spaces, aka complete normed vector spaces and bounded linear operators on normed vector spaces. Highlights of the course include the following:
The Hahn-Banach theorem. The open mapping theorem. The closed graph theorem. Banach-Steinhaus theorem also known as the uniform boundedness principle. Dual spaces. Weak convergence. The Banach-Alaoglu theorem. The spectral theorem for compact self-adjoint operators.