Wigner-type theorem on symmetry transformations in type II factors

Wigner's theorem on symmetry transformations can be formulated in the follo wing way. If phi is a bijective map on the set of all nonzero minimal proje ctions in a type I factor A which preserves transition probabilities with r espect to a faithful normal semifinite trace, then it can be extended to a linear *-automorphism or to a linear *-antiautomorphism of A. In this paper we prove a natural analogue of this statement for type II factors.