Lifts of Operator Systems

TL;DR

This paper extends the theory of slack operators and sums-of-squares criteria to operator systems, investigating conditions under which their enveloping $C^*$-algebras are finite-dimensional or images of finite-dimensional systems.

Contribution

It introduces a novel transfer of lift theory from convex cones to operator systems, enabling new analysis of their $C^*$-algebra properties.

Findings

Characterization of finite-dimensional enveloping $C^*$-algebras

Conditions for operator systems to be linear images of finite-dimensional systems

Extension of sums-of-squares criteria to operator systems

Abstract

We transfer the theory of slack operators and sums-of-squares-criteria for lifts from convex cones to operator systems. These allow to study the following question, among others: Given an abstract operator system, is its enveloping $C^*$-algebra finite-dimensional, or is it the linear image of a system with a finite-dimensional enveloping algebra?