The Measure Algebra of the Heisenberg Group

Irreducible representations of the convolution algebraM(Hn) of bounded regular complex Borel measures on the Heisenberg group Hnare analyzed. For the Segal–Bargmann representationρ, theC*-algebra generated byρ[M(Hn)] is just theC*-algebra generated by Berezin–Toeplitz operators with positive-definite “symbols.” This algebra is a deformation of the sup norm algebra generated by positive-definite functions on complexn-space Cn.