  Let M be a factor of type III with separable predual and with normal states
phi_1,...,phi_k, 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 phi_i 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 II_1 instead of type III holds.
