Additive subgroups of topological vector spaces / Wojciech Banaszczyk
Type de document : Livre numériqueCollection : Lecture notes in mathematics, 1466Langue : anglais.Éditeur : Berlin : Springer-Verlag, 1991ISBN: 9783540539179.ISSN: 1617-9692.Sujet MSC : 43A35, Abstract harmonic analysis, Positive definite functions on groups, semigroups, etc.46A11, Functional analysis - Topological linear spaces and related structures, Spaces determined by compactness or summability properties
47Bxx, Operator theory - Special classes of linear operators
22B05, Locally compact abelian groups, General properties and structure of LCA groupsEn-ligne : Springerlink | Zentralblatt | MathSciNet
Chapter 1 has a preliminary character, and it contains standard results on topological abelian groups and their relations with subgroups of the additive group of a topological vector space. Chapter 2 contains results on exotic groups, i.e. abelian topological groups without nontrivial continuous unitary representations. Chapter 3 is devoted to nuclear groups and their relations with nuclear locally convex spaces. Chapter 4 is devoted to the Bochner theorem and Chapter 5 is devoted to the Pontryagin duality. A distinction is made between known and new at the end of each section. (MathSciNet)
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