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Last update: G_M (16.05.2012)
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Last update: G_M (27.04.2012)
An introductory course in functional analysis. |
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Last update: G_M (27.04.2012)
W. Rudin: Analýza v reálném a komplexním oboru, Academia, Praha, 2003
J. Lukeš: Úvod do funkcionální analýzy, skripta MFF
J. Lukeš: Zápisky z funkcionální analýzy, skripta MFF |
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Last update: G_M (27.04.2012)
lecture and exercises |
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Last update: prof. RNDr. Ivan Netuka, DrSc. (05.09.2013)
1. Linear spaces
algebraic version of Hahn-Banach theorem
2. Hilbert spaces (a survey of results from the course in mathematical analysis :
orthogonal projection; orthogonalization; abstract Fourier series; representation of Hilbert space
3. Normed linear spaces; Banach spaces
bounded linear operators and functionals; representation of bounded linear functionals in a Hilbert space; Hahn-Banach theorem; dual space; reflexivity; Banach-Steinhaus theorem; open map theorem and closed graph theorem; inverse operator; spectrum of the operator; compact operator; examples of Banach spaces and their duals (integrable functions, continuous functions)
4. Locally convex spaces
Hahn-Banach theorem and separation of convex sets; weak convergence; weak topology; examples of locally convex spaces (continuous functions, differentiable functions)
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