a1 Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA; Email: (email@example.com)
Let be a von Neumann algebra acting on a Hilbert space and let be a von Neumann subalgebra of . If is singular in for every Hilbert space , is said to be completely singular in . We prove that if is a singular abelian von Neumann subalgebra or if is a singular subfactor of a type-II1 factor , then is completely singular in . is separable, we prove that is completely singular in if and only if, for every θAut(′) such that θ(X)=X for all X ′, θ(Y)=Y for all Y′. As the first application, we prove that if is separable (with separable predual) and is completely singular in , then is completely singular in for every separable von Neumann algebra . As the second application, we prove that if 1 is a singular subfactor of a type-II1 factor 1 and 2 is a completely singular von Neumann subalgebra of 2, then is completely singular in .
(Received August 16 2007)
2000 Mathematics subject classification