$JW$-factors and antiautomorphisms of von Neumann algebras

The connection between $JW$-factors and their enveloping von Neumann algebras is studied for $JW$-factors not isomorphic to the Hermitian part of any von Neumann algebra. It is proved that these $JW$-factors are determined by an involutive $^*$-antiautomorphism of the enveloping von Neumann algebra. A classification of $JW$-factors of type III according to types III$_\lambda$, $0\leqslant\lambda\leqslant1$, is given, and the existence of each type is proved. It is shown that there are only two nonisomorphic $JW$-factors of type II$_1$ for which the enveloping von Neumann algebras are hyperfinite.
Bibliography: 18 titles.