For countable discrete amenable groups, strict comparison holds in A ⊗ K where A is l^∞(Γ) ⋊ Γ or C(M) ⋊ Γ with M the universal minimal set: d_τ(a) < d_τ(b) for all traces τ implies a is Cuntz subequivalent to b.
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Minimal sufficient Jordan algebras generated by Neyman-Pearson tests characterize sufficiency for positive trace-preserving maps, implying Petz-like recovery and equivalence of interconversion conditions for quantum dichotomies.
Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.
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Strict comparison holds in the uniform Roe algebra of a discrete amenable group
For countable discrete amenable groups, strict comparison holds in A ⊗ K where A is l^∞(Γ) ⋊ Γ or C(M) ⋊ Γ with M the universal minimal set: d_τ(a) < d_τ(b) for all traces τ implies a is Cuntz subequivalent to b.
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Sufficiency and Petz recovery for positive maps
Minimal sufficient Jordan algebras generated by Neyman-Pearson tests characterize sufficiency for positive trace-preserving maps, implying Petz-like recovery and equivalence of interconversion conditions for quantum dichotomies.
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On free components of Artin and Coxeter groups
Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.