This article is cited in 3 papers

$JW$-factors and antiautomorphisms of von Neumann algebras

Sh. A. Ayupov


Abstract: 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.

UDC: 517.98

MSC: Primary 46L70; Secondary 46L35, 46L40

Received: 10.03.1983

 English version: Mathematics of the USSR-Izvestiya, 1986, 26:1, 201–209

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