What it is about
You will learn the basics of functional analysis in Banach and Hilbert spaces. In the end you will be able to analyze linear functionals and bounded as well as compact self-adjoint operators, understand duality, and apply concepts such as weak and weak* convergence.
What you will be able to do
- Understanding Banach and Hilbert spaces
- Analyzing bounded linear operators
- Applying the open mapping theorem and Hahn-Banach theorem
- Investigating the spectrum of compact self-adjoint operators
- Understanding duality and weak and weak* convergence
- Basic knowledge of unbounded operators
What the module consists of
- LecturesConveying the theoretical content and demonstrative examples
- Übung/Practice sessionsDeepening through exercises sheets, solutions and gradually independent work
Teaching method
- LecturesPresentation of content, examples and discussion for motivation and orientation
- Übungen/Practice sessionsMastering the methods on exercises, starting under guidance, later independent work in groups