Let $H(X):=(\R \times X) \leftthreetimes X^*$ 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 $G:=H(L_4[0,1])$ is reflexively representable but weakly
continuous unitary representations of $G$ in Hilbert spaces do not separate points of $G$. This answers the question of A. Shtern.
Heisenberg group, unitary representation, minimal topological group, relatively minimal subgroup, weakly almost periodic, positive definite, reflexive space.
MSC 2000: 22A05, 43A60, 54H10