PřF:M7980 Selected topics of functional

M7980 Selected topics of functional analysis

Faculty of Science
Autumn 2010

Extent and Intensity

2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Teacher(s)

prof. Alexander Lomtatidze, DrSc. (lecturer)

Guaranteed by

Timetable

Mon 14:00–15:50 M6,01011

Prerequisites

Linear functional analysis.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives

The aim of the course is to explain certain selected topics of functional analysis, which are not usually scheduled in standard university courses.

Syllabus

Bair classification. Uniform convergence and related topics. Consequences of the Hahn-Banach theorem. Representation of functionals in special spaces. Compactness criteria in special spaces. Universality of the space of continuous functions. Banach-Mazur theorem. Weak convergence and related topics. Banach spaces with base.

Literature

KOLMOGOROV, Andrej Nikolajevič and Sergej Vasil‘jevič FOMIN. Základy teorie funkcí a funkcionální analýzy. Translated by Vladimír Doležal - Zdeněk Tichý. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1975, 581 s. info
LJUSTERNIK, Lazar‘ Aronovič and Vladimir Ivanovič SOBOLEV. Elementy funkcional'nogo analiza. 2. perer. izd. Moskva: Nauka, 1965, 519 s. info
DUNFORD, Nelson and Jacob T. SCHWARTZ. Linejnyje operatory : obščaja teorija. Edited by A. G. Kostjučenko, Translated by L. I. Golovnoj - B. S. Mitjagin. Moskva: Izdatel'stvo inostrannoj literatury, 1962, 895 s. info

Teaching methods

lectures

Assessment methods

Teaching: Lecture 2 hours a week. Exam: oral.

Language of instruction

Czech

Further comments (probably available only in Czech)

The course is taught only once.