Logo ČVUT
CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

Selected Topics in Functional Analysis

The course is not on the list Without time-table
Code Completion Credits Range
01VPFN Z,ZK 5 2P+2C
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Mathematics
Synopsis:

Abstract:

Basic notions and results are addressed concerning successively topological spaces, metric spaces, topological vector

spaces, normed and Banach spaces, Hilbert spaces.

Requirements:

aktivní účast na cvičení, písemná a ústní zkouška

Syllabus of lectures:

Outline:

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
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet6966306.html