Unitary operators in the orthogonal complement of a type I von Neumann subalgebra in a type II1 factor
- 论文类型：期刊论文
- 发表刊物：Journal of Mathematical Analysis and Applications
- 收录刊物：SCIE、Scopus
- 卷号：416
- 期号：1
- 页面范围：390-401
- ISSN号：0022-247X
- 关键字：Type II1 factor; Type I von Neumann algebra; Conditional expectation; Orthogonal complement; Unitary operator
- 摘要：It is well-known that the equality
L-G circle minus L-H = (span{L-g: g is an element of G - H}(SOT)) over bar
holds for G an i.c.c. group and H a subgroup in G, where L-G and L-H are the corresponding group von Neumann algebras and L-G circle minus L-H is the set {x is an element of L-G: E-LH(x) = 0} with E-LH the conditional expectation defined from L-G onto L-H. Inspired by this, it is natural to ask whether the equality
N circle minus A = ( span{u: u is unitary in N circle minus A}(SOT)) over bar
holds for N a type II1 factor and A a von Neumann subalgebra of N. In this paper, we give an affirmative answer to this question for the case A a type I von Neumann algebra. (C) 2014 Elsevier Inc. All rights reserved. - 发表时间：2014-08-01