Generalized Heisenberg groups and Shtern's question

Details Generalized Heisenberg groups and Shtern's question Generalized Heisenberg groups and Shtern's question

2004-11-06

arxiv.org/abs/math/0411137v1

Mathematics

Functional Analysis

7 pages

Scientific paper

Let H(X) be the generalized Heisenberg group induced by a normed space X. We
prove that X is a relatively minimal subgroup of H(X). We show that the group
$G:=H(L_4[0,1])$ is reflexively representable but weakly continuous unitary
representations of G in Hilbert spaces do not separate points of G. This
answers a question of A. Shtern.

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