Uniqueness of extremal almost periodic states on the injective type III${}_1$ factor

Michael Hartglass, Brent Nelson

Let $R_{\infty }$ denote the Araki--Woods factor -- the unique separable injective type III${}_1$ factor. For extremal almost periodic states $\phi ,\psi \in (R_{\infty }{)}_{\ast }$, we show that if $…