Year: 2026
Type: preprint
Abstract: We construct counterexamples to Arveson's hyperrigidity conjecture for operator systems in commutative $C^*$-algebras. In each example, every irreducible representation of the $C^*$-envelope is a boundary representation, but hyperrigidity fails. The first example is the operator system of continuous affine functions on an infinite-dimensional weighted $\ell^p$ ball. In the second infinite-dimensional example, we start with commuting operators and construct a nontrivial dilation. The final example comes from a compact truncated epigraph of a strictly convex function and yields a finite-dimensional operator system.
Source: arXiv (Cornell University)
Authors: Bilich, Boris, Scherer, Marcel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223057077