OAI/Analysis/KadisonKastler/PublishedBicentralizerInputs.lean

State-theoretic hypotheses for the expected subfactor

Connes–Størmer, Homogeneity of the state space of factors of type III₁, J. Functional Analysis 28 (1978), 187–196, main state-orbit transitivity theorem, gives the faithful vector-state specialization below.

Marrakchi, Full factors, bicentralizer flow and approximately inner automorphisms, arXiv:1811.10253v2, Theorem D(ii), gives the second input. It is stated only for the fixed Powers product used by the application.

Together, these hypotheses imply the existence of the full expected matrix subfactor, without an additional relative-algebra hypothesis.