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Course, academic year 2023/2024
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Selected Topics on Functional Analysis - NMMA342
Title: Vybrané partie z funkcionální analýzy
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2023
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: doc. RNDr. Bohumír Opic, DrSc.
Class: M Bc. OM
M Bc. OM > Povinně volitelné
M Bc. OM > Zaměření STOCH
Classification: Mathematics > Functional Analysis
Pre-requisite : {One 2nd year Analysis course}
Incompatibility : NMMA331, NRFA075
Interchangeability : NMMA331, NRFA075
Is incompatible with: NMMA942
Is pre-requisite for: NMSA351
Is interchangeable with: NRFA075, NMMA942
In complex pre-requisite: NMSA349
Annotation -
Last update: G_M (16.05.2012)
An introductory course in functional analysis for bachelor's program in General Mathematics, specialization Stochastics.
Aim of the course -
Last update: G_M (27.04.2012)

An introductory course in functional analysis.

Course completion requirements
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".

Literature -
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

Teaching methods -
Last update: G_M (27.04.2012)

lecture and exercises

Requirements to the exam
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.

Syllabus -
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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