Course: Functional Analysis II

« Back
Course title Functional Analysis II
Course code MU/02026
Organizational form of instruction Not filled in + Not filled in
Level of course Bachelor
Year of study 3
Semester Summer
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory-optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • AVERBUCH Vladimír, DrSc.
  • JAHN Jiří, Mgr. Ph.D.
Course content
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).

Learning activities and teaching methods
unspecified
Recommended literature
  • A. N. Kolmogorov, S. V. Fomin. Základy teorie funkcí a funkcionální analýzy. Praha, SNTL, 1975.
  • V. I. Averbuch. Functional Analysis, pomocné učební texty MÚ SU. MÚ SU, Opava, 1999.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Mathematical Institute in Opava Mathematics (2014-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (2) Economy 3 Summer
Mathematical Institute in Opava Mathematical Analysis (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics (2014-IVT) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics in Risk Management (3) Mathematics courses 3 Summer
Mathematical Institute in Opava Applied Mathematics (2014-F) Mathematics courses 3 Summer
Mathematical Institute in Opava Mathematical Methods in Economics (3) Economy 3 Summer