MU02026 Functional Analysis II

Mathematical Institute in Opava
Summer 2014
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
RNDr. Jiří Jahn, Ph.D. (seminar tutor)
Guaranteed by
Vladimír Averbuch, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU02023 Logic and Set Theory || 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
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).
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, Summer 2013, Summer 2015, Summer 2016, Summer 2017, Summer 2018, Summer 2019, Summer 2020, Summer 2021, Summer 2022, Summer 2023, Summer 2024.
  • Enrolment Statistics (Summer 2014, recent)
  • Permalink: https://is.slu.cz/course/sumu/summer2014/MU02026