MATS2220 Banach Spaces (5 cr)
Study level:
Advanced studies
Grading scale:
0-5
Language:
English, Finnish
Responsible organisation:
Department of Mathematics and Statistics
Curriculum periods:
2024-2025, 2025-2026, 2026-2027, 2027-2028
Description
Banach spaces, duality in Banach spaces, Hahn–Banach theorem, Baire category theorem, Banach–Steinhaus theorem, open mapping theorem, weak and weak-star topology.
Learning outcomes
After completing the course the student:
- Masters the basic theory of Banach spaces.
- Has obtained skills to use Banach spaces in modern analysis.
Description of prerequisites
Topology,
Hilbert Spaces
Study materials
lecture notes
Andrew M. Bruckner, Judith B. Bruckner, and Brian S. Thomson, Real Analysis, 2008, www.classicalrealanalysis.com
Avner Friedman, Foundations of modern analysis, Dover Publications Inc. 1982; ISBN: 0-486-64062-0
Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications, Wiley, 2013; ISBN: 1-118-62639-7
Lauri Kahanpää, Funktionaalianalyysi, luntomoniste 51, Matematiikan ja tilastotieteen laitos, Jyväskyän yliopisto, 2004.; ISBN: 951-39-1763-0 (in Finnish)
Lecture notes of the course
Literature
- Haïm Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer, 2010; ISBN: 2-010-93838-2
- John B. Conway, A course in functional analysis (2nd edition), Springer, 1990; ISBN: 0-387-97245-5
Completion methods
Method 1
Evaluation criteria:
Course exam and exercises
Time of teaching:
Period 4
Select all marked parts
Method 2
Evaluation criteria:
Final exam. The score must be at least half of the maximum score.
Select all marked parts
Parts of the completion methods
x
Participation in teaching (5 cr)
Type:
Participation in teaching
Grading scale:
0-5
Language:
English, Finnish
Teaching
3/17–5/25/2025 Lectures
x
Exam (5 cr)
Type:
Exam
Grading scale:
0-5
Language:
English, Finnish