Abstract
Studying Pukánszky’s type III factor,M2{M_2}, 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 abelianII∞{\text {II}_\infty }factors. The extension (by ampliation) of central sequences in a finite factor,N, toM⊗NM \otimes Nis shown to be central. Also, we give two examples of the reduction (by equivalence) of a central sequence inM⊗NM \otimes Nto a sequence inN. Finally, applying the definition of asymptotic abelianness ofC∗{C^\ast }-algebras toW∗{W^\ast }-algebras leads to the conclusion that all factors satisfying this property are abelian.
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