Michael Hartz, FernUniversität in Hagen
"Dilations in finite dimensions and matrix convexity"
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 classical dilation theorems have been established by several authors.
I will talk about an abstract dilation result for completely positive maps on finite dimensional operator systems. This result shows when an infinite dimensional dilation theorem has a finite dimensional cousin. Moreover, I will explain how these questions are related to matrix convexity. This is joint work with Martino Lupini.
MC 5501