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An introductory course in functional analysis for bachelor's program in General Mathematics, specialization
Stochastics.
Last update: G_M (16.05.2012)
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An introductory course in functional analysis. Last update: G_M (27.04.2012)
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The credit for exercises is awarded provided the student enrolls in the course. The credit from exercises is required to participate at the exam. The exam consists of a written computational part and oral theoretical part. Students failing in the test are not allowed to continue with the oral part. Students failing in the oral part must go through both parts (written and oral) in their next attempt. Last update: Honzík Petr, doc. Mgr., Ph.D. (30.09.2025)
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W. Rudin: Analýza v reálném a komplexním oboru, Academia, Praha, 2003
M. Fabian, P. Habala, P. Hájek, V. Montesions Santalucía, J. Pelant and V. Zizler: Banach space theory (the basis for linear and nonlinear analysis), Springer-Verlag New York, 2011 Last update: Cúth Marek, doc. Mgr., Ph.D. (28.01.2022)
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lecture and exercises Last update: G_M (27.04.2012)
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Ability to solve problem similar to those solved at the exercises, knowledge of the theory presented in the lecture, understanding. Last update: Honzík Petr, doc. Mgr., Ph.D. (30.09.2025)
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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)
Last update: Netuka Ivan, prof. RNDr., DrSc. (05.09.2013)
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