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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Functional Analysis 1

The course is not on the list Without time-table
Code Completion Credits Range Language
01FANA1 Z,ZK 5 2P+2C Czech

In order to register for the course 01FAN2, the student must have successfully completed or received credit for and not exhausted all examination dates for the course 01FANA1.

Garant předmětu:
Lecturer:
Tutor:
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:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-05-18
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