MU02029 Functional Analysis and Optimalization II

Mathematical Institute in Opava
Summer 2013
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
Teacher(s)
Vladimír Averbuch, DrSc. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
Vladimír Averbuch, DrSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU02028 Functional Anal. and Opt. 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 of the basic course of functional analysis are duality in Hausdorff locally convex spaces, elements of convex analysis and 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 convexes spaces (basic operators of convex analysis, Duality Theorem, weak compactness of polars and subdifferentials, Alaoglou-Bourbaki Theorem).
    3. Applications to normed spaces (dual normed space, theorem on norm-preserving extension, reflexive spaces).
    4. Hilbert spaces (theorem on orthogonal projection and their 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 (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012.
  • Enrolment Statistics (recent)
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