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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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RULES FOR THE ACADEMIC YEAR 2024/25
The credit from exercises is required to participate at the exam. Condition for obtaining credit for excercises: two successfully written exams during the semester. In case student is not successfull in the written exams, it is possible to obtain credit also for additional homeworks. In this case the student must contact the teacher. Some more details may be found in the section "Requirements to the exam". For more information check the homepage below: https://www2.karlin.mff.cuni.cz/~cuth/VPFA_pozadavky.pdf Last update: Cúth Marek, doc. Mgr., Ph.D. (13.09.2024)
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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. Details at the web page of the lecturer: https://www.karlin.mff.cuni.cz/~cuth/VPFA_pozadavky.pdf Last update: Cúth Marek, doc. Mgr., Ph.D. (13.09.2024)
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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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