Abstract
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.
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