Lifts of Operator Systems

2025/08/21 by Dannemüller, Markus, Netzer, Tim
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2508.15348

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?

Citations

• The set of separable states has no finite semidefinite representation\n except in dimension 3\× 2
• Spectrahedral shadows
• An elementary and constructive solution to Hilbert's 17th Problem for matrices

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• Model Theory of Operator Systems and C^*-Algebras
• The lifting property for C^*-algebras : from local to global ?
• Exactness and LLP Results via Operator System Methods
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• Four-dimensional operator systems without the lifting property