MS-E1462: Banach Spaces (Extended Exercise Set)
Course details
| Course name | Banach Spaces |
|---|---|
| Course code | MS-E1462 |
| Credits | 5 |
| Period | N/A |
| Lecturer | Ville Turunen |
| Completion method | Extended exercise set |
Description
The main focus is on Banach spaces which could be treated as generalized versions of Hilbert spaces.
Learning outcomes official
You will learn about norms and seminorms in infinite-dimensional vector spaces. Related to these structures, you will understand basic properties of bounded linear operators, duality and spectral theory in Banach spaces.
Content official
Bounded linear operators, compact linear operators, functionals, and elementary spectral theory in Banach spaces (Riesz Compactness Theorem, Zabreiko’s Lemma, Uniform Boundedness Principle, Open Mapping and Closed Graph Theorems, Hahn-Banach Theorem, Gelfand’s Spectral Theorem).
Course material
Official material
There are quite good lecture notes (the same one used in Hilbert Spaces), available as PDF written in LaTeX, which are enough for the course.
Extra material
Contents and workload
Compared to other master’s level courses and even the contact teaching version of this course, this completion method is quite easy.
There is a home exam of 20 problems, or in other words, a large exercise set. To complete the course one must “solve all of the exercises well enough”.
Overall workload
Related courses
Official prerequisites
Additional prerequisites
MS-E1461: Hilbert Spaces (Recommended but not mandatory)
Timestamp
Based on the 2025 version of the course.