On the structure of real injective $W^*$-factors of type III$_{\lambda}$, $0\lambda1$

A. A. Rakhimov

Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 26, Tome 255 (1998), pp. 148-163

Résumé

We consider $*$-automorphisms and $*$-antiautomorphisms of real and complex factors. We establish both the uniqueness of the class of $*$-automorphisms (with $\mod(\cdot )=\lambda$, $\lambda\ne1$) of a real injective II$_\infty$ factor and the uniqueness of the class of $*$-antiautomorphisms (with$\mod(\cdot )=\sqrt{\lambda}$, $\lambda\ne1$) of a complex injective II$_\infty$ factor. It is well known that for complex factors the notions of hyperfiniteness and injectivity are equivalent. Here we prove that for real factors the two notions are no longer equivalent.