Operator systems for tolerance relations on finite sets

DOI10.1016/J.INDAG.2022.12.009arXiv2207.07735MaRDI QIDQ6405129

Walter D. van Suijlekom, Mick Gielen

Publication date: 15 July 2022

Abstract: We study the duals of a certain class of finite-dimensional operator systems, namely the class of operator systems associated to tolerance relations on finite sets or equivalently the class of operator systems that are associated with graphs. In the case where the graphs associated with these operator systems are chordal we are able to find concrete realizations of their duals as sitting inside of finite-dimensional $C^{*}$-algebras. We then use these concrete realizations to compute the $C^{*}$-envelopes, propagation numbers and extremal rays of these duals in the chordal case. Finally, we exemplify our results by applying them to operator systems of band matrices.

Mathematics Subject Classification ID

Nonparametric tolerance and confidence regions (62G15) Noncommutative algebraic geometry (14A22) (H)-spaces and duals (55P45) General theory of (C^*)-algebras (46L05) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

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