Von Neumann algebras as complemented subspaces of B(H)

被引：1
|
作者：
Christensen, Erik [1 ]
Wang, Liguang [2 ]
机构：
[1] Univ Copenhagen, Dept Math Sci, DK-1168 Copenhagen, Denmark
[2] Qufu Normal Univ, Sch Math Sci, Qufu, Shandong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF MATHEMATICS | 2014年 / 25卷 / 11期
关键词：
Type II1 factor; fundamental group; hyperfinite type II1 factor; injective von Neumann algebra; complemented subspace; RINGS; OPERATORS;
D O I：
10.1142/S0129167X14501079
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let M be a von Neumann algebra of type II1 which is also a complemented subspace of B( H). We establish an algebraic criterion, which ensures that M is an injective von Neumann algebra. As a corollary we show that if M is a complemented factor of type II1 on a Hilbert space H, then M is injective if its fundamental group is nontrivial.
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页数：9
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