Generalized Heisenberg groups and Shtern's question
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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