Friday, August 5, 2022 — 10:00 AM EDT

Nicholas Manor, Department of Pure Mathematics, University of Waterloo

"Nonunital Operator Systems and Noncommutative Convexity"

The recent work on nc (noncommutative) convex sets of Davidson-Kennedy and Kennedy-Shamovich show that there is a rich duality between the category of operator systems and the category of compact nc convex sets, leading to new insights even in the case of C*-algebras.

The category of nc convex sets is a generalization of the usual notion of a compact convex set that provides meaningful connections between convex theoretic notions and notions in operator system theory.

In this talk, we present an analogous duality theorem for norm closed self-adjoint subspaces of B(H).  Using this duality, we will describe various C*-algebraic and operator system theoretic notions, as well as a rich class of examples arising as duals of well-understood operator systems. This is joint work with Matthew Kennedy and Se-Jin Kim.

Online. Contact Nick Manor (nmanor@uwaterloo.ca) for more information.

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