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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 2012 to 2014
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

Guarantor:	prof. RNDr. Ivan Netuka, DrSc.
Teacher(s):	doc. RNDr. Roman Lávička, Ph.D. prof. RNDr. Ivan Netuka, DrSc. Mgr. Dalibor Šmíd, Ph.D.
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 interchangeable with:	NRFA075, NMMA942
In complex pre-requisite:	NMSA349

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

An introductory course in functional analysis for bachelor's program in General Mathematics, specialization Stochastics.

Last update: G_M (16.05.2012)

Aim of the course -

An introductory course in functional analysis.

Last update: G_M (27.04.2012)

Literature - Czech

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

Last update: Bárta Tomáš, doc. RNDr., Ph.D. (23.05.2019)

Teaching methods -

lecture and exercises

Last update: G_M (27.04.2012)

Syllabus -

1. Linear spaces

algebraic version of Hahn-Banach theorem

2. Hilbert spaces

orthogonal projection; orthogonalization; abstract Fourier series; representation of Hilbert space

3. Normed linear spaces; Banach spaces

bounded linear operators and functionals; 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; Stone-Weierstrass theorem)

4. Locally convex spaces

Hahn-Banach theorem and separation of convex sets; weak convergence; weak topology; extremal point and the Krein-Milman theorem; examples of locally convex spaces (continuous functions, differentiable functions)

Last update: Netuka Ivan, prof. RNDr., DrSc. (05.09.2013)