OAI/Analysis/KadisonKastler/PublishedExpectedMatrixSubfactor.lean

The expected hyperfinite subfactor consequence used for preparation

Marrakchi, Full factors, bicentralizer flow and approximately inner automorphisms, arXiv:1811.10253v2, Theorem D(ii), gives trivial bicentralizer for a type III₁ factor absorbing R_lambda. Haagerup, Connes' bicentralizer problem and uniqueness of the injective factor of type III₁, Acta Math. 158 (1987), Lemma 3.8 and the proof of Theorem 3.1, (2) => (3), pp.142--145, then gives an irreducible hyperfinite II₁ subfactor with faithful normal expectation. Its increasing full-matrix model is retained here.

The composed trace-state has a cyclic separating vector in the given separable type III representation: Haagerup, The standard form of von Neumann algebras, Math. Scand. 37 (1975), Lemma 2.10(1), p.278, and Blackadar III.1.7.9 give the representation transfer. This input concerns a single algebra and contains no proximity or perturbation conclusion.