MU02023 Functional Analysis I

Mathematical Institute in Opava
Winter 2018
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
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
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).
Literature
    recommended literature
  • V. I. Averbuch. Functional Analysis, pomocné učební texty MÚ SU. MÚ SU, Opava, 1999. info
  • A. N. Kolmogorov, S. V. Fomin. Základy teorie funkcí a funkcionální analýzy. Praha, SNTL, 1975. info
Language of instruction
Czech
Further Comments
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1997, Summer 1998, Winter 1998, Summer 1999, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2019, Winter 2020, Winter 2021.
  • Enrolment Statistics (Winter 2018, recent)
  • Permalink: https://is.slu.cz/course/sumu/winter2018/MU02023