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.
Niu.Z-stability of transformation group C*-algebras.Trans
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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.