Additive Subgroups of Topological Vector Spaces (Lecture Notes in Mathematics) - Softcover

Banaszczyk, Wojciech

9780387539171: Additive Subgroups of Topological Vector Spaces (Lecture Notes in Mathematics)

Softcover

ISBN 10: 0387539174 ISBN 13: 9780387539171

Publisher: Springer Verlag, 1991

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 L�vy-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.

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