Groups of quasi-invariance and the Pontryagin duality ✩

By Saak Gabriyelyan. 2008

47 citations recorded by the source corpus.

Abstract A Polish group G is called a group of quasi-invariance or a QI-group, if there exist a locally compact group X and a probability measure μ on X such that (1) there exists a continuous monomorphism ϕ from G into X with dense image, and (2) for each g ∈ X either g ∈ ϕ ( G ) and the shift μ g is equivalent to μ or g ∉ ϕ ( G ) and μ g is orthogonal to μ . It is proved that ϕ ( G ) is a σ -compact subset of X . We show that there exists a Polish non-locally quasi-convex (and hence nonreflexive) QI-group such that its bidual is not a QI-group. It is proved also that the bidual group of a QI-group may be not a saturated subgroup of X . It is constructed a reflexive non-discrete group topology on the integers.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4e2752d1de112c068f76dab9697a77de3015e181

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1. Saak Gabriyelyan
2. A. Leiderman
3. Jerzy Kakol

Citations in the corpus

• On topological groups with a small base and metrizability (2015, background): “Then A(e) is a countable, reflexive [38, 21], kω (and hence hemicompact) [40, 4.”