##### Venue: Department of Mathematics, Lecture Hall I

In this talk, we shall define $\\Gamma$-contractions, which were introduced by Jim Agler and Nicholas Young. We shall construct an explicit $\\Gamma$-isometric dilation of a $\\Gamma$-contraction and produce a genuine functional model. A crucial operator equation has to be solved for constructing such a dilation. We shall show how the existence of such a solution characterizes a $\\Gamma$-contraction. This solution, which is unique, also provides a complete unitary invariant.

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Last updated: 06 Mar 2020