Subjects

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Selected Topics on Functional Analysis (O) - NMMA942

Title:	Vybrané partie z funkcionální analýzy (O)
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2017
Semester:	summer
E-Credits:	5
Hours per week, examination:	summer s.:2/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Is provided by:	NMMA342

Guarantor:	prof. RNDr. Ivan Netuka, DrSc.
Classification:	Mathematics > Functional Analysis
Incompatibility :	NMMA342, NRFA075, NRFA175
Interchangeability :	NMMA342, NRFA175
Is interchangeable with:	NRFA175

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: G_M (16.05.2012)

An introductory course in functional analysis. Not equivalent to the course NMMA342.

Aim of the course -

Last update: G_M (27.04.2012)

An introductory course in functional analysis.

Literature - Czech

Last update: G_M (27.04.2012)

W. Rudin: Analýza v reálném a komplexním oboru, Academia, Praha, 2003

J. Lukeš: Úvod do funkcionální analýzy, skripta MFF

J. Lukeš: Zápisky z funkcionální analýzy, skripta MFF

Teaching methods -

Last update: G_M (27.04.2012)

lecture and exercises

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)