Arveson's hyperrigidity conjecture is false

Boris Bilich; Adam Dor-On

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arXiv · 2404.05018

Arveson's hyperrigidity conjecture is false

Boris Bilich·Adam Dor-On

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Abstract

Arveson's hyperrigidity conjecture predicts that if the non-commutative Choquet boundary of a separable operator system $\mathcal{S}$ is the entire spectrum of its generated C*-algebra $\mathcal{B}$ then $\mathcal{S}$ is hyperrigid in $\mathcal{B}$. We provide a counterexample to the conjecture with a C*-algebra $\mathcal{B}$ of type I generated by a single operator.

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Boris Bilich, Adam Dor-On. 2024-04-07. Arveson's hyperrigidity conjecture is false. https://arxiv.org/abs/2404.05018

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