MATS2220 Banach-avaruudet, kevät 2026

Overview

The course Banach spaces takes place at the University of Jyväskylä starting on 16.03.2026 and until 24.05.2026. Please consult the official page of the course on Sisu. On this TIM page you will find all the weekly assignments and the preliminary lecture notes of the course. Please find the schedule of the lectures and other communication on this website. Should you have questions related to the lectures or the exercises, please contact me at giovanni.g.covi@jyu.fi and/or the teaching assistant at shubham.s.jaiswal@jyu.fi.

Contents

We will start with a reminder about the main points of the previous course (Hilbert spaces), in particular dual spaces. We will then see the main results in Banach spaces theory, namely the Banach-Steinhaus theorem, the open mapping theorem, and various forms of the celebrated Hahn-Banach theorem. Finally, we will study the weak topology.

Modalities of exam

Evaluation for the course can be obtained in one of the following ways:

  • 100% from final - You only take part to the final exam, and your grade is the grade of the exam.

  • 50% from weekly assignments, 50% from final - You solve the weekly assignments and you take part to the final exam. Your grade is the average of the two. Each problem from the assignments is given 2 points (perfect or almost perfect solution), 1 point (honest attempt) or 0 points (no solution, or very wrong solution). The grade from the assignments is obtained as percentage of points obtained over all available points.

Exercises

The exercise sessions happen on Monday afternoon. The solutions to the exercises must be given before the beginning of the session to the teaching assistant Shubham Jaiswal either in person (at lecture or in room MaD234) or by email (shubham.s.jaiswal@jyu.fi). If preferred, points can also be obtained by coming to the weekly exercise sessions and presenting one's work at the blackboard. In this case, one does not need to present any written assignment.

Lecture notes

These are the preliminary lecture notes of the course (in Finnish). Please observe that there may still be errors. The redacted version will appear at the end of the course.

# runner
# harjoitushyvitykset
# harjoitushyvitystenTyhjennys
# arvostelufunktioLaskeSummaTentti2
# runner2
# arvostelufunktioKT1
# arvostelunTyhjennysTentti1

These are the current permissions for this document; please modify if needed. You can always modify these permissions from the manage page.