Normal states of type III factors

الأصل · EN

Let M be a factor of type III with separable predual and with normal states phi₁,...,phiₖ, omega with omega faithful. Let A be a finite dimensional C*-subalgebra of M. Then it is shown that there is a unitary operator u in M such that phiᵢ Ad u =omega on A for i=1,...,k. This follows from an embedding result of a finite dimensional C*-algebra with a faithful state into M with finitely many given states. We also give similar embedding results of C*-algebras and von Neumann algebras with faithful states into M. Another similar result for a factor of type II₁ instead of type III holds.