The main subjects of this course are complete normed vector spaces and bounded (continuous) linear operators. Highlights of the course include the following:
* The open mapping theorem. * The closed graph theorem. * The Banach-Steinhaus theorem (the uniform boundedness principle). * The Hahn-Banach theorem. * Dual spaces. * Weak convergence. * The Banach-Alaoglu theorem. * The spectral theorem for bounded self-adjoint operators.
- Literature: Erwin Kreyszig, Introductory functional analysis with applications, ISBN 0471504599.