# MU:MU02025 Functional Analysis I - Course Information

## MU02025 Functional Analysis I

**Mathematical Institute in Opava**

Winter 2016

**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 **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**- Mathematical Analysis (programme MU, M1101)
- 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 the spaces equipped with compatible algebraic 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 (conservation of algebraical properties by topological operations, properties of neighbourhoods of zero in a topological vector space, continuous linear mappings 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 (Fréchet spaces, Banach theorem on open mapping, Banach theorem on inverse mapping, theorem on closed graph).

4. Boundedness principle (bounded sets, bounded operators, equicontinuity, equiboudedness and pointwise boundedness, Banach-Steinhaus theorem).

- 1. Topological vector spaces (conservation of algebraical properties by topological operations, properties of neighbourhoods of zero in a topological vector space, continuous linear mappings of topological vector spaces).
**Literature****Language of instruction**- Czech
**Further Comments**- The course can also be completed outside the examination period.

- Enrolment Statistics (Winter 2016, recent)
- Permalink: https://is.slu.cz/course/sumu/winter2016/MU02025