Pontryagin duality for subgroups and quotients of nuclear spaces

DOI10.1007/BF01472136zbMath0593.46006MaRDI QIDQ1076280

Wojciech Banaszczyk

Publication date: 1986

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164078

zbMATH Keywords

dual groupPontryagin dualitydually embeddedadditive topological groupcountable products of nuclear Fréchet spacesdually closedequicontinuous subsetEvery nuclear Fréchet space is strongly reflexive as anEvery nuclear Fréchet space is strongly reflexive as an additive topological grouptopology of uniform convergence on precompact sets

Mathematics Subject Classification ID

Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Duality theory for topological vector spaces (46A20) Duality theorems for locally compact groups (22D35)

Related Items (6)

Inequalities for convex bodies and polar reciprocal lattices in \(\mathbb{R}^ n\) ⋮ On local quasi-convexity as a three-space property in topological abelian groups ⋮ Characteristic functionals of probabilistic measures in DS-groups and related topics ⋮ A survey on reflexivity of abelian topological groups ⋮ Quaternion-valued positive definite functions on locally compact abelian groups and nuclear spaces ⋮ New bounds in some transference theorems in the geometry of numbers

Cites Work

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• The space \(\mathcal D(\Omega)\) is not \(B_r\)-complete
• Extensions of the Pontrjagin duality. I: Infinite products
• Zur Dualitätstheorie projektiver Limites abelscher Gruppen
• On the existence of unitary representations of commutative nuclear Lie groups
• The Pontrjagin Duality Theorem in Linear Spaces
• Closed subgroups of nuclear spaces are weakly closed
• Countable products and sums of lines and circles: their closed subgroups, quotients and duality properties
• k-Groups and Duality

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