MU:MU02026 Functional Analysis II - Course Information
MU02026 Functional Analysis II
Mathematical Institute in OpavaSummer 2017
- Extent and Intensity
- 2/2/0. 6 credit(s). Type of Completion: zk (examination).
- 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)
- MU02023 Functional Analysis I || MU02025 Functional Analysis I
- 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)
- Applied Mathematics in Risk Management (programme MU, B1101)
- Mathematical Analysis (programme MU, M1101)
- Mathematical Methods in Economics (programme MU, B1101)
- Mathematics (programme MU, B1101)
- Course objectives
- The subjects of the second part of the basic course of functional analysis are duality in Hausdorff locally convex spaces, elements of convex analysis and the theory of normed spaces and Hilbert spaces.
- Syllabus
- 1. Duality theory (duality in Hausdorff locally convex spaces, weak and weakened topologies).
2. Convex analysis in locally convex topological vector spaces (basic operators of convex analysis, Duality theorem, theorem on weak compactness of polars and subdiferentials, Alaoglu-Bourbaki theorem).
3. Applications to normed spaces (dual normed spaces, Banach theorem on the norm-preserving extension, reflexive spaces).
4. Hilbert spaces (theorem on orthogonal projection and its corollaries, Hilbert basis).
- 1. Duality theory (duality in Hausdorff locally convex spaces, weak and weakened topologies).
- Literature
- Language of instruction
- Czech
- Further Comments
- The course can also be completed outside the examination period.
- Enrolment Statistics (Summer 2017, recent)
- Permalink: https://is.slu.cz/course/sumu/summer2017/MU02026