M7980 Selected topics of functional analysis

Faculty of Science
Autumn 2010 - only for the accreditation
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
prof. Alexander Lomtatidze, DrSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
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.
The course is also listed under the following terms Autumn 2006, Autumn 2008, Autumn 2010, Autumn 2011 - acreditation.