Additive subgroups of topological vector spaces
Additive subgroups of topological vector spaces
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拓扑向量空间的可加子群
DOI：
10.1007/bfb0089147
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发表时间：
1991
影响因子：
1.2
通讯作者：
W. Banaszczyk
中科院分区：
文献类型：
--
作者：
W. Banaszczyk
已知关于正定函数的Pontryagin-van Kampen型对偶定理和Bochner定理对于某些非局部紧的交换拓扑群是成立的。这本书致力于系统地呈现现有的材料。它基于核群的原始概念，它包括LCA群和核局部凸空间及其加子群、商群和乘积。对于(可度量化的、完备的)核群，我们得到了关于级数重排的庞特里亚金对偶定理、Bochner定理和Lévy-Steinitz定理的类似结果(回答了S.Ulam的一个老问题)。这本书是用泛函分析的语言写的。所用的方法主要取自数几何、Banach空间几何和拓扑代数。读者应该只知道泛函分析和抽象调和分析的基础知识。
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.