In [2] W. Banaszczyk introduced nuclear groups, a Hausdorff variety of abelian topological groups which is generated by all nuclear vector groups (cf. 2.3) and which contains all nuclear vector spaces and all locally compact abelian groups.
We prove in 5.6 that the Hausdorff variety generated by all nuclear vector spaces and all locally compact abelian groups (denoted by 𝒱₁) is strictly smaller than the Hausdorff variety of all nuclear groups (denoted by 𝒱₂). More precisely,...
We prove that every locally quasi-convex Schwartz group satisfies the Glicksberg theorem for weakly compact sets.
Abstract
For a topological group G, the group G* of continuous homomorphisms (characters) into :=z∈ℂ: |z| = 1 endowed with the compact-open topology is called the character group of G and G is named ( Pontryagin) reflexive if the canonical homomorphism , x ↦ (χ ↦ χ(x)), is a topological isomorphism. A comprehensive exposition of duality theory is given here.
In particular, settings closely related to the theory of vector spaces (like local quasi-convexity and the corresponding hull) are studied...
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