Separable type III_1 factors with trivial bicentralizer are selfless W*-probability spaces for every faithful normal state.
Okayasu , A note on injective factors with trivial bicentralizer
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Selfless W$^*$-probability spaces and Connes' bicentralizer problem
Separable type III_1 factors with trivial bicentralizer are selfless W*-probability spaces for every faithful normal state.