Course for international guest/part time students

Faculty

Faculty of Science

Organization

TTK Department of Applied Analysis and Computational Mathematics

Code

topvtb1u0um17em

Title

Topological vector spaces and Banach algebras (l)

Usual semester

Autumn

Published semester

2025/26/2

ECTS

3

Language

hu

Learning outcomes

Knowledge: Acquisition of fundamental concepts and methods related to locally convex spaces and normed algebras. Ability: Understanding and application of basic techniques in the theory of locally convex spaces and normed algebras. Attitude: A commitment to expanding mathematical knowledge, acquiring and developing new mathematical insights and competencies. A drive to apply mathematical knowledge as broadly as possible. Autonomy and responsibility: Ability to independently choose appropriate methods for solving various problems, based on a solid foundation in functional analysis. An awareness of the importance of precise mathematical thinking and concept formation, as well as the limitations of the applicability of functional analysis.

Course content

The aim of the course is to introduce the basic elements of topological vector spaces and normed algebras, including: metrizable topological vector spaces, locally convex spaces, the Hahn–Banach theorem and related results, weak topologies, the Banach–Alaoglu and Alaoglu–Bourbaki theorems, duality theory (bounded and convex sets, the Mackey–Arens theorem), the general Banach–Steinhaus theorem in barrelled spaces. Additionally, the foundations of distribution theory are covered, including strict inductive limits of locally convex spaces. The course also addresses specific topics of practical importance and introduces related applications.

Assessment method

exam grade, practical grade (5-point scale)

Bibliography

lecture notes

Recommended bibliography

–  H. Schaefer: Topological vector spaces, Springer Verlag, 2001. –  W. Rudin, Funcional analysis, McGraw Hill, 1991.

Programmes of the course