Asymptotic Abelianness of Infinite Factors
نویسنده
چکیده
Studying Pukanszky's type III factor, M2, we show that it does not have the property of asymptotic abelianness and discuss how this property is related to property L. We also prove that there are no asymptotic abelian II factors. The extension (by ampliation) of central sequences in a finite factor, N, to M ® N is shown to be central. Also, we give two examples of the reduction (by equivalence) of a central sequence in M ® zV to a sequence in N. Finally, applying the definition of asymptotic abelianness of C -algebras to W*algebras leads to the conclusion that all factors satisfying this property are abelian.
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