Functional Analysis 1

Code	Completion	Credits	Range	Language
01FANA1	Z,ZK	5	2P+2C	Czech

Relations:

Course guarantor:

Pavel Šťovíček

Lecturer:

Pavel Šťovíček

Tutor:

Pavel Šťovíček

Supervisor:

Department of Mathematics

Synopsis:

Requirements:

Syllabus of lectures:

1. Topological spaces

2. Metric spaces, compactness criteria, completion of a metric space

3. Topological vector spaces

4. Minkowski functional, the Hahn-Banach theorem

6. Metric vector spaces, Fréchet spaces

6. Normed vector spaces, bounded linear mappings, the operator norm

7. Banach spaces, extension of a bounded operator

8. Banach spaces of integrable functions

9. Hilbert spaces, orthogonal projection, orthogonal basis

10. The Riesz representation theorem, adjoint operator

Syllabus of tutorials:

Study Objective:

Study materials:

Key references:

[1] J. Blank, P. Exner, M. Havlíček: Hilbert Space Operators in Quantum Physics, Springer, 2008.

[2] B. Simon: Operator Theory: A Comprehensive Course in Analysis, Part 4, AMS, Rhode Island, 2015.

[3] K. Yoshida, Functional Analysis, Springer Science & Business Media, New York 2013

[4] J. B. Conway, A Course in Functional Analysis, Springer Science & Business Media, New York 2013

Recommended references:

[5] W. Rudin: Real and Complex Analysis, (McGrew-Hill, Inc., New York, 1974)

[6] A. N. Kolmogorov, S. V. Fomin: Elements of the Theory of Functions and Functional Analysis, (Dover Publications,

1999)

[7] A. E. Taylor: Introduction to Functional Analysis, (John Wiley and Sons, Inc., New York, 1976)

Note:

Time-table for winter semester 2024/2025:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomTR:212 Šťovíček P. 16:00–17:50 (lecture parallel1) Trojanova 13
Wed	roomTR:212 Šťovíček P. 08:00–09:50 (parallel nr.101) Trojanova 13
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: