Unitary operators in the orthogonal complement of a type I von Neumann subalgebra in a type II1 factor

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Shi, Rui¹  Zhou, Xiaoyan¹ 

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

关键词: Type II1 factor;    Type I von Neumann algebra;    Conditional expectation;    Orthogonal complement;    Unitary operator;   

DOI  :  10.1016/j.jmaa.2014.02.020

来源: Elsevier

【 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.

【 授权许可】

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