Generalized heisenberg groups and shtern's question

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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 languageEnglish
Pages (from-to)775-782
Number of pages8
JournalGeorgian Mathematical Journal
Issue number4
StatePublished - Jan 2004


  • Heisenberg group
  • minimal topological group
  • positive definite
  • reflexive space
  • relatively minimal subgroup
  • unitary representation
  • weakly almost periodic


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