Analysis Seminar: "Dilations in finite dimensions"
Abstract: Dilation theorems make it possible to represent fairly general operators on Hilbert space as pieces of better understood operators on a larger Hilbert space. However, in classical dilation results such as Sz.-Nagy's dilation theorem, the dilation typically acts on an infinite dimensional space, even if the original operator lives in finite dimensions. To remedy this drawback, finite dimensional versions of some classical dilation theorems have been established by Egervary, McCarthy--Shalit and others.
I will talk about an abstract result which shows when an infinite dimensional dilation theorem has a finite dimensional cousin. Moreover, I will explain how this result is related to questions in matrix convexity. This is joint work with Martino Lupini.
Host: John McCarthy