Generalized heisenberg groups and shtern's question

M. Megrelishvili

doi:10.1515/gmj.2004.775

Generalized heisenberg groups and shtern's question

M. Megrelishvili

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

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	https://doi.org/10.1515/gmj.2004.775
State	Published - Jan 2004

Keywords

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

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10.1515/gmj.2004.775

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AB - 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.

KW - Heisenberg group

KW - minimal topological group

KW - positive definite

KW - reflexive space

KW - relatively minimal subgroup

KW - unitary representation

KW - weakly almost periodic

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Generalized heisenberg groups and shtern's question

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Keywords

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