We provide an explicit normal distinguished boundary dilation to a pair of commuting operators (S,P) having the closed symmetrized bidisc Γ as a spectral set. This is called Sz.-Nagy dilation of (S,P). The operator pair that dilates (S,P) is obtained by an application of Stinespring dilation of (S,P) given by Agler and Young. We further prove that the dilation is minimal and the dilation space is no bigger than the dilation space of the minimal unitary dilation of the contraction P. We also describe model space and model operators for such a pair (S,P).

The author was supported in part by a postdoctoral fellowship of the Skirball Foundation via the Center for Advanced Studies in Mathematics at Ben-Gurion University of the Negev.