Additive subgroups of topological vector spaces / Wojciech Banaszczyk

Auteur: Banaszczyk, Wojciech (1954-) - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics, (Online) ; 1466Langue: anglaisÉditeur: Berlin : Springer-Verlag, 1991 ISBN: 9783540539179 ISSN: 1617-9692Note: 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) Sujets MSC: 46A11 Functional analysis -- Topological linear spaces and related structures -- Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.)
43A35 Abstract harmonic analysis -- Abstract harmonic analysis -- Positive definite functions on groups, semigroups, etc
47Bxx Operator theory -- Special classes of linear operators
22B05 Topological groups, Lie groups -- Locally compact abelian groups (LCA groups) -- General properties and structure of LCA groups
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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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