| W~*-三元算子环的摄动 |
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| 引用本文： | 阮忠进,王利广.W~*-三元算子环的摄动[J].数学学报,2017,60(1):53-60. |
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| 作者姓名： | 阮忠进 王利广 |
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| 作者单位： | 1. 伊利诺伊大学厄巴纳-香槟分校数学系 美国 61801;
2. 曲阜师范大学数学科学学院 曲阜 273165 |
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| 基金项目： | 国家自然科学基金资助项目（11371222，11671133）；Simons Foundation（281192） |
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| 摘 要： | 本文证明了:如果两个W~*-三元算子环V和W的cb距离d_(cb)(V,W)很小的时候,其连接冯·诺依曼代数之间的距离也很小.还证明了:和内射的W~*-三元算子环靠的很近的W~*-三元算子环也是内射的.对具有r性质和McDuff性质的W~*-三元算子环,类似的结论也成立.
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| 关 键 词： | W~*-三元算子环 Ⅱ_1型因子 Γ性质 McDuff因子 |
Perturbation of W*-ternary Ring of Operators |
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| Zhong Jin RUAN,Li Guang WANG.Perturbation of W*-ternary Ring of Operators[J].Acta Mathematica Sinica,2017,60(1):53-60. |
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| Authors: | Zhong Jin RUAN Li Guang WANG |
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| Institution: | 1. Department of Mathematics, University of Illinois, Urbana, Illinois 61801, USA;
2. School of Mathematical Sciences, Qufu Normal University, Qufu 273165, P. R. China |
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| Abstract: | We show that when the cb-distance dcb(V, W) between two W*-ternary ring of operators V and W is small, the distance between their linking von Neumann algebras R(V) and R(W) is also small.We show that W*-ternary ring of operators close to injective W*-ternary ring of operators is injective again.We also consider similar properties for W*-ternary ring of operators with property Γ or McDuff property. |
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| Keywords: | W*-ternary ring factor of type Ⅱ1 property Γ McDuff factor |
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