The $$C^{*}$$ C ∗ -algebras of connected real two-step nilpotent Lie groups

Abstract

Using the operator valued Fourier transform, the \(C^{*}\)-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier transform of such \(C^{*}\)-algebras fulfills the norm controlled dual limit property.