MU:MU02028 Functional Anal. and Opt. I - Course Information
MU02028 Functional Analysis and Optimalization I
Mathematical Institute in OpavaWinter 2012
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: z (credit).
- Teacher(s)
- Vladimír Averbuch, DrSc. (lecturer)
RNDr. Jiří Jahn, Ph.D. (seminar tutor) - Guaranteed by
- Vladimír Averbuch, DrSc.
Mathematical Institute in Opava - Prerequisites (in Czech)
- MU00004 && MU00006 PC User Practice
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Applied Mathematics (programme MU, B1101)
- Mathematics (programme MU, B1101)
- Course objectives
- The main attention of the first part of the basic course of functional analysis is given to topological vector spaces, i.e. to spaces, equipped with compatible algebraical and topological structures, to continuous linear mappings of such spaces and to three basic principles of functional analysis: Hahn?Banach Theorem, openness principle and boundedness principle.
- Syllabus
- 1. Topological vector spaces (conservations of algebraical properties by topological operations, properties of neighbourhoods of zero in a topological vector space, continuous linear mapping of topological vector spaces).
2. Hahn-Banach Theorem (convex sets, convex functions, Jensen inequality, sublinear functions, Minkowski function, Hahn-Banach Theorem, locally convex spaces, semi-norms, locally convex topology generated by semi-norms, strict separation theorem).
3. Openness principle (F-spaces, Banach Theorem on open mapping, Banach Theorem on inverse mapping, theorem on closed graph).
4. Boundedness principle (bounded sets, bounded operators, equicontinuity, equiboundedness and pointwise boundedness, Banach-Steinhaus theorem).
- 1. Topological vector spaces (conservations of algebraical properties by topological operations, properties of neighbourhoods of zero in a topological vector space, continuous linear mapping of topological vector spaces).
- Literature
- Language of instruction
- Czech
- Further comments (probably available only in Czech)
- The course can also be completed outside the examination period.
- Enrolment Statistics (recent)
- Permalink: https://is.slu.cz/course/sumu/winter2012/MU02028