Type II1 factors satisfying the spatial isomorphism conjecture.
Type II1 factors satisfying the spatial isomorphism conjecture.
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II1型因子满足空间同构猜想。
DOI：
10.1073/pnas.1217792109
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发表时间：
2012
影响因子：
11.1
通讯作者：
Cameron J
中科院分区：
文献类型：
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作者：
Cameron J
本文提出了 Kadison 和 Kastler 的工作中的一个猜想 [Kadison RV, Kastler D (1972) Am J Math 94: 38–54]，希尔伯特空间上的冯诺依曼代数 M 应该酉等价于每个足够接近的冯诺依曼代数 N，而且，可以选择接近于恒等算子的实现酉。已知该猜想对于适用的冯诺依曼代数是正确的，并且在本文中，我们描述了该猜想有效的不可命名因子的类别。这些类基于超有限 II1 因子与适当选择的离散群的阿贝尔代数的叉积的张量积。
This paper addresses a conjecture in the work by Kadison and Kastler [Kadison RV, Kastler D (1972) Am J Math 94: 38–54] that a von Neumann algebra M on a Hilbert space should be unitarily equivalent to each sufficiently close von Neumann algebra N, and, moreover, the implementing unitary can be chosen to be close to the identity operator. This conjecture is known to be true for amenable von Neumann algebras, and in this paper, we describe classes of nonamenable factors for which the conjecture is valid. These classes are based on tensor products of the hyperfinite II1 factor with crossed products of abelian algebras by suitably chosen discrete groups.