Additive Subgroups of Topological Vector Spaces

1991
ISBN: 978-3-540-53917-9
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1466, 182 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 300 g

Reihe: Lecture Notes in Mathematics

The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.

Zielgruppe

Research

Autoren/Hrsg.

Banaszczyk, Wojciech

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

Preliminaries.- Exotic groups.- Nuclear groups.- The bochner theorem.- Pontryagin duality.