|
Lecturer(s)
|
-
Brzezina Miroslav, doc. RNDr. CSc., dr. h. c.
|
|
Course content
|
1, 2. Linear vector spaces, linear operators, functionals and properties 3. Metric spaces, complete metric spaces 4. Normed linear spaces, continuous linear operators 5. Spaces with scalar product, orthogonality. 6. Continuous linear operators in normed linear spaces 7. Closed linear operators 8. Linear continuous functionals 9. The principle of uniform boundedness, convergence of linear continuous operators 10. Dual spaces. Projections 11. Continuous linear operators in Hilbert spaces. Symmetric and discontinuous operators 12. Orthogonal projections. Spectrum. 13. Compact operators, basic properties Topics for seminars follow that of the lectures.
|
|
Learning activities and teaching methods
|
Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
|
|
Learning outcomes
|
Introductory course of functional analysis. Banach and Hilbert spaces. Linear operator, functional. Basic principles of linear functional analysis. Compact operators.
Introduction to functional analysis. Banach and Hilbert spaces. Linear operator, functional. Basic principles of linear functional analysis. Compact operators.
|
|
Prerequisites
|
basics of mathematical analysis
|
|
Assessment methods and criteria
|
Combined examination
Basic knowledge of spaces, mappings and principles of functional analysis
|
|
Recommended literature
|
-
Najzar, K.:. Funkcionální analýza. [skripta] Praha, SPN 1988..
-
Rudin, W.:. Analýza v reálném a komplexním oboru. Praha, Academia 1977..
-
Taylor, E.:. Úvod do funkcionální analýzy. Praha, Academia 1973..
|