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

x

Exam (5 cr)

Type:
Exam
Grading scale:
0-5
Language:
English, Finnish
No published teaching