Introduction to Functional Analysis
- Students will be introduced to the basic notions and the basic principles of Functional Analysis.
- Apply the basic principles of Functional Analysis in concrete situations
- Calculate the norms of linear operators
- Find the spectra of linear operators by using, in particular, duality theory
- Identify the duals of concrete Banach spaces and operators
- Prove the compactness or noncompactness of concrete operators
- Prove the completeness of classical function spaces
- Normed and Banach spaces, bounded linear maps.
- Hilbert spaces
- The Hahn-Banach Theorem, the Open Mapping Theorem, the Uniform Boundedness Principle
- Basic duality theory
- Elementary spectral theory
- Compact operators. The Hilbert-Schmidt Theorem
- midterm gradeThe midterm exam (oral) will be at the end of October (or at the beginning of November) and will include only the material of the 1st module.
- exercise sheets gradeTo get the maximum grade for the exercise sheets, you should solve 75% of all the exercises. If you solve more, you will earn bonus points. You can also earn bonus points for working actively at the exercise classes and for solving «bonus exercises» (marked as «B» in the sheets).
- final examThe oral exam will be at the end of December and will include only the material of the 2nd module.
- 2021/2022 1st module
- 2021/2022 2nd module0.35 * exercise sheets grade + 0.3 * final exam + 0.35 * midterm grade