The hyperfinite II₁-factor is Ulam stable in the trace norm on the unit ball, via a dimension-free matrix algebra result, implying isolation under approximate *-isomorphisms.
Ulam stability for classes of nuclear C*-algebras
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abstract
We study Ulam stability for approximate *-homomorphisms of C*-algebras. We prove stability results for several classes of nuclear C*-algebras with respect to von Neumann algebra targets, including abelian C*-algebras and large classes arising in the Elliott classification program. We also discuss permanence properties, counterexamples, and related stability phenomena. As applications, we obtain rigidity and independence results for corona algebras.
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2026 1verdicts
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The hyperfinite II$_1$-factor is Ulam stable
The hyperfinite II₁-factor is Ulam stable in the trace norm on the unit ball, via a dimension-free matrix algebra result, implying isolation under approximate *-isomorphisms.