New York Journal of Mathematics
Volume 20 (2014) 645-664


Sourav Pal

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

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Published: June 22, 2014
Keywords: Symmetrized bidisc, Spectral sets, Normal distinguished boundary dilation, Operator models
Subject: 47A13, 47A15, 47A20, 47A25, 47A45


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.

Author information

Department of Mathematics, Ben-Gurion University of the Negev, Be'er Sheva-84105, Israel.