Additive subgroups of topological vector spaces
Author(s)
Bibliographic Information
Additive subgroups of topological vector spaces
（Lecture notes in mathematics, 1466）
Springer-Verlag, c1991
- : gw
- : us
Available at / 85 libraries
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Library & Science Information Center, Osaka Prefecture University
: gwNDC8:410.8||||10009594885
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
L/N||LNM||14669109009S
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
DC19:515/B222070201060
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Note
Bibliography: p. [168]-173
Includes indexes
Description and Table of Contents
Description
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 Levy-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.
Table of Contents
Preliminaries.- Exotic groups.- Nuclear groups.- The bochner theorem.- Pontryagin duality.
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