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We provide an explicit normal distinguished boundary dilation to a pair ofcommuting operators $(S,P)$ having the closed symmetrized bidisc $\Gamma$ as aspectral set. This is called Sz.-Nagy dilation of $(S,P)$. The operator pairthat 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 minimaland the dilation space is no bigger than the dilation space of the minimalunitary dilation of the contraction $P$. We also describe model space and modeloperators for such a pair $(S,P)$.

From Stinespring dilation to Sz.-Nagy dilation on the symmetrized bidisc and operator models