The course builds on Functional Analysis I and studies various topics in more depth.
We focus on two topics
1) Operator theory
Here we study consequences of the spectral theorem which we recall in the first lectures. We will show that how self-adjoint positive operators arise from positive closed form and in a next step study Dirichlet forms. We study then further aspects of operator theory such as the discrete/essential spectrum and min-max principles, holw to exploit symmetry of operators and the Riesz-Thorin theorem.
2) Locally convex vector spaces
We first start to study or recall basics in topology such as separation axioms, Urysohns and Tietzes theorem, metrizability, compactness and Tychonoffs theorem. We then have a deeper look at locally convex spaces with the aim to prove the Krein-Milman theorem and Choquet's theorem.
- Kursleiter*in: Philipp Bartmann
- Kursleiter*in: Prof. Dr. Matthias Keller
- Kursleiter*in: Matti Richter