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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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To obtain the credit, students are required to successfully pass two credit tests. A resit test will be offered for each of the credit tests. If a student fails the resit test, the credit may still be obtained by submitting solutions to assigned problems. The final examination consists of a written problem-solving part and an oral theoretical part. Further information will be available on the lecturer’s webpage. Last update: Pick Luboš, prof. RNDr., CSc., DSc. (02.10.2026)
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The primary source of study should be the lecture notes. The material can also be supplemented by, for example, the following references.
Last update: Pick Luboš, prof. RNDr., CSc., DSc. (02.10.2026)
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lecture and exercises Last update: G_M (27.04.2012)
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The examination consists of two parts: a written part and an oral part. In order to take the oral part, the student must successfully pass the written part. The written examination will consist of computational problems based on the material covered during the semester. Students will register for the oral examination electronically through the SIS system. If a student does not pass the written part and therefore cannot proceed to the oral part of the examination, they will have the opportunity, at the designated time, to review their written work and become acquainted with its detailed evaluation. During the oral part of the examination, the student will be asked to formulate one definition, state two theorems, and prove one of them. Furthermore, the student will be expected to demonstrate an understanding of the definition and the stated theorems. Last update: Pick Luboš, prof. RNDr., CSc., DSc. (02.10.2026)
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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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