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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. Bohumír Opic, DrSc. (26.01.2024)
The credit from exercises is required to participate at the exam.
Condition for obtaining credit for excercises: active 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. RNDr. Bohumír Opic, DrSc. (26.01.2024)
Ability to solve problem similar to those solved at the exercises, knowledge of the theory presented in the lecture, understanding. |
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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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