A new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable Hilbert space
A new proof of the equivalence of injectivity and hyperfiniteness for factors on a separable Hilbert space
复制标题
可分离希尔伯特空间上因子的单射性和超有限性等价性的新证明
DOI：
10.1016/0022-1236(85)90002-3
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发表时间：
1985
影响因子：
1.7
通讯作者：
U. Haagerup
中科院分区：
文献类型：
--
作者：
U. Haagerup
A。证明了可分离希尔伯特空间上的内射因子是超有限的基本结果。本文给出了对这一结果的一个新的证明，该证明避开了cones证明中最技术性的部分。特别是证明不依赖于自同构群论。该方法的出发点是Wassermann对单射半离散代数的简单证明，以及Choi和Effros对半离散冯·诺伊曼代数的描述，即n × n矩阵上的单位映射具有近似完全正分解的冯·诺伊曼代数。
In 1975 A. Connes proved the fundamental result that injective factors on a separable Hilbert space are hyperfinite. In this paper a new proof of this result is presented in which the most technical parts of Connes proof are avoided. Particularly the proof does not rely on automorphism group theory. The starting point in this approach is Wassermann's simple proof of injective ⇒ semidiscrete together with Choi and Effros' characterization of semidiscrete von Neumann algebras as those von Neumann algebrasNfor which the identity map onNhas an approximate completely positive factorization throughn × n-matrices.