Title: Dilations, functional model and a complete unitary invariant of a $\Gamma$-contraction
Speaker: Sourav Pal Department of Mathematics, IISc
Date: 21 November 2011
Time: 3:30-4:30 p.m.
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.