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

摘要

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