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Analysis SeminarExport this event to calendar

Friday, February 12, 2016 — 3:30 PM EST

Adam Dor On, Department of Pure Mathematics, University of Waterloo

“Matrix convex sets: Inclusions, dilations and completely positive interpolation”

A matrix convex set is a stratified set of the form S = n1Sn, where each Sn is comprised of d-tuples of n × n matrices, and is closed under application of unital completely positive maps from Mn to Mk. Our main tools are polar duality in the sense of Effros and Winkler, and constructions of commuting normal dilations in the sense of Helton, Klep, McCullough and Schweighofer.

Given two matrix convex sets S and T , we find geometric conditions on S or on T , to ensurethatS1 ⊂T1 impliesS⊂C·T forsomeconstantC>0.

Under various symmetry conditions on S we can guarantee that C = d, the number of variables. We show that d is sharp for the maximal matrix ball Wmax(B ). We then find and

Our results have implications to spectrahedral inclusion problems studied by Helton, Klep, McCullough and Schweighofer, and to existence of interpolating unital completely positive maps.
The first 20 minutes of this talk should be accessible to graduate students outside of analysis.
This is joint work with Ken Davidson, Orr Shalit and Baruch Solel.

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