Indexed by: Journal Article
Date of Publication: 2014-08-01
Journal: Journal of Mathematical Analysis and Applications
Included Journals: Scopus、SCIE
Volume: 416
Issue: 1
Page Number: 390-401
ISSN: 0022-247X
Key Words: Type II1 factor; Type I von Neumann algebra; Conditional expectation; Orthogonal complement; Unitary operator
Abstract: 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.