关于具有McDuff性质和Γ性质因子摄动的注记

A note on the perturbation of McDuff factors and factors with propertyΓ

设L是一个有可分预对偶的Ⅱ1型因子,τ是L的一个正规的忠实的迹态.则L的所有具有Γ性质的子因子构成的集合与L的所有McDuff子因子构成的集合在由迹诱导的Hausdorff距离d 2下是既开又闭的.

In this short note,we show that when L is a typeⅡ1 factor with separable predual andτis the normal faithful tracial state of L,the set of subfactors of L with propertyΓand the set of all McDuff subfactors of L are open and closed in the Hausdorff metric d 2 induced by the trace norm.