MU:MU02025 Functional Analysis I - Course Information

MU02025 Functional Analysis I

Extent and Intensity

2/2/0. 6 credit(s). Type of Completion: z (credit).

Teacher(s)

RNDr. Jiří Jahn, Ph.D. (lecturer)
doc. RNDr. Michaela Mlíchová, Ph.D. (seminar tutor)

Guaranteed by

RNDr. Jiří Jahn, Ph.D.
Mathematical Institute in Opava

Course Enrolment Limitations

The course is offered to students of any study field.

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

Study Materials
The course can also be completed outside the examination period.

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