Additive subgroups of topological vector spaces /

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Bibliographic Details
Author / Creator:Banaszczyk, Wojciech, 1954-
Imprint:Berlin ; New York : Springer-Verlag, ©1991.
Description:1 online resource (vi, 178 pages) : illustrations.
Language:English
Series:Lecture notes in mathematics, 0075-8434 ; 1466
Lecture notes in mathematics (Springer-Verlag) ; 1466.
Subject:
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11069644
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ISBN:9783540463962
3540463968
0387539174
9780387539171
3540539174
9783540539179
Notes:Includes bibliographical references (pages 168-173) and indexes.
Restrictions unspecified
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Print version record.
Summary: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 Lvy-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.
Other form:Print version: Banaszczyk, Wojciech, 1954- Additive subgroups of topological vector spaces. Berlin ; New York : Springer-Verlag, ©1991 0387539174