Abstract
Let H(X) ≔ (ℝ × X) ⋋ X* be the generalized Heisenberg group induced by a normed space X. We prove that X and X* are relatively minimal subgroups of H(X). We show that the group G ≔ H(L4[0; 1]) is reflexively representable but weakly continuous unitary representations of G in Hilbert spaces do not separate points of G. This answers the question of A. Shtern.
| Original language | English |
|---|---|
| Pages (from-to) | 775-782 |
| Number of pages | 8 |
| Journal | Georgian Mathematical Journal |
| Volume | 11 |
| Issue number | 4 |
| DOIs | |
| State | Published - Jan 2004 |
Keywords
- Heisenberg group
- minimal topological group
- positive definite
- reflexive space
- relatively minimal subgroup
- unitary representation
- weakly almost periodic