Course: Functional Analysis I

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Course title Functional Analysis I
Course code MU/02025
Organizational form of instruction Not filled in + Not filled in
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction Czech
Status of course Compulsory
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
  • AVERBUCH Vladimír, DrSc.
  • JAHN Jiří, Mgr. Ph.D.
Course content
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).

Learning activities and teaching methods
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 Mathematical Analysis (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (1-IVT) Mathematics courses 3 Winter
Mathematical Institute in Opava Mathematics (2-F) Mathematics courses 3 Winter