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Motivated by the successful dilation theory for a pair of commuting bounded operators which has the symmetrized bidisc $\Gamma$ as a spectral set, this talk explores the dilation and functional model for a non-commuting tuple of bounded operators which satisfies a natural condition. Matrix valued Toeplitz operators play a big role. Explicit dilation using Toeplitz operators is constructed under very few conditions, i.e., with a large amount of generality. Consequently, it can be applied to several commuting cases. The dilation and model theory is surprisingly successful even in the non-commuting case simply on the basis of solvability of a system of operator equations. |