MU02028 Functional Analysis and Optimalization I

Mathematical Institute in Opava
Winter 2012
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
Vladimír Averbuch, DrSc. (lecturer)
RNDr. Jiří Jahn, Ph.D. (seminar tutor)
Guaranteed by
Vladimír Averbuch, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU00004 && MU00006 PC User Practice
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 spaces, equipped with compatible algebraical 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 (conservations of algebraical properties by topological operations, properties of neighbourhoods of zero in a topological vector space, continuous linear mapping 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 (F-spaces, Banach Theorem on open mapping, Banach Theorem on inverse mapping, theorem on closed graph).
    4. Boundedness principle (bounded sets, bounded operators, equicontinuity, equiboundedness 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 (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011.
  • Enrolment Statistics (recent)
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