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arXiv · 2610.34269

Operator systems in étale groupoid C*-algebras

Georgios Baziotis·Douglas Farenick·Evgenios T. A. Kakariadis·Malte Leimbach·Lyudmila Turowska·Walter D. van Suijlekom
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Abstract

We study operator systems arising from positivity domains of étale groupoids with compact unit space. Extending Kavruk's enough unitaries principle we show that such operator systems are hyperrigid in the C$^*$-algebra they generate. We focus on operator systems of positivity domains in UHF algebras and, by identifying them with Cantor graph operator systems, we show that they are hyperrigid. Furthermore, we show that in general, such a characterization is not possible when the étaleness condition of the underlying groupoid is removed, due to the failure of reduced spectral and compact operator synthesis.

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Georgios Baziotis, Douglas Farenick, Evgenios T. A. Kakariadis, Malte Leimbach, Lyudmila Turowska, Walter D. van Suijlekom. 2026-10-25. Operator systems in étale groupoid C*-algebras. https://arxiv.org/abs/2610.34269

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