On the properties of some sets of von Neumann algebras under perturbation

来源 :Operator Algebra and Harmonic Analysis(三亚国际论坛算子代数和谐波分析) | 被引量 : 0次 | 上传用户：lich1234554321

【摘要】

：

　　Let L be a type II1 factor with separable predual and τ a normal faithful tracial state of L.We first show that the set of subfactors of L with property Γ

【作者】

：

Liguang Wang

【机构】

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QufuNormalUniversity

【出处】

：

Operator Algebra and Harmonic Analysis(三亚国际论坛算子代数和谐波分析)

【发表日期】

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2015年5期

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　　Let L be a type II1 factor with separable predual and τ a normal faithful tracial state of L.We first show that the set of subfactors of L with property Γ,the set of type II1 subfactors of L with similarity property and the set of all McDuff subfactors of L are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2.

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On the properties of some sets of von Neumann algebras under perturbation

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