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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: doc. RNDr. Michal Johanis, Ph.D. (11.02.2023)
The credit from exercises is required to participate at the exam.
Condition for obtaining credit for excercises: at least 66% attendance at excercises.
Some more details may be found in the section "Requirements to the exam". |
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Last update: doc. Mgr. Marek Cúth, Ph.D. (28.01.2022)
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 |
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Last update: G_M (27.04.2012)
lecture and exercises |
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Last update: doc. Mgr. Marek Cúth, Ph.D. (28.01.2022)
Ability to solve problem similar to those solved at the exercises, knowledge of the theory presented in the lecture, understanding. Details at the web page of the lecturer. |
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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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