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Last update: G_M (16.04.2010)
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Last update: G_M (16.04.2010)
An introductory course in functional analysis. |
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Last update: G_M (16.04.2010)
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 (16.04.2010)
lecture and exercises |
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Last update: G_M (16.04.2010)
1. Linear spaces algebraic version of Hahn-Banach theorem
2. Hilbert spaces orthogonal projection; orthogonalization; abstract Fourier series; representation of Hilbert space
3. Normed linear spaces; Banach spaces bounded linear operators and functionals; 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; Stone-Weierstrass theorem)
4. Locally convex spaces Hahn-Banach theorem and separation of convex sets; weak convergence; weak topology; extremal point and the Krein-Milman theorem; examples of locally convex spaces (continuous functions, differentiable functions) |