关于有限von Neumann代数的相对可修性的一个注记

IF 0.7 4区数学 Q2 MATHEMATICS

Journal of Operator Theory Pub Date : 2018-12-15 DOI:10.7900/jot.2017dec06.2200

Xiaoyan Zhou, Junsheng Fang

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引用次数: 1

摘要

设M是有限的von Neumann代数（分别为II1型因子），设N⊂M是II1因子（分别为N⊆M具有原子部分）。我们证明了如果包含N⊂M是可接受的，则通过保迹正规酉完全正映射，暗示M上的单位映射通过Mm（C）⊗N具有近似因子分解，这是Haagerup的一个结果的推广。我们还证明了可调和内含物的两个永久性性质。一个是弱Haagerup性质，另一个是较弱的精确性。

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A note on relative amenability of finite von Neumann algebras

Let M be a finite von Neumann algebra (respectively, a type II1 factor) and let N⊂M be a II1 factor (respectively, N⊂M have an atomic part). We prove that if the inclusion N⊂M is amenable, then implies the identity map on M has an approximate factorization through Mm(C)⊗N via trace preserving normal unital completely positive maps, which is a generalization of a result of Haagerup. We also prove two permanence properties for amenable inclusions. One is weak Haagerup property, the other is weak exactness.

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来源期刊

Journal of Operator Theory 数学-数学

CiteScore

1.30

自引率

12.50%

发文量

审稿时长

12 months

期刊介绍： The Journal of Operator Theory is rigorously peer reviewed and endevours to publish significant articles in all areas of operator theory, operator algebras and closely related domains.