A construction of equivalence subrelations for intermediate subalgebras. (English) Zbl 1033.46046

Aoi, Hisashi

J. Math. Soc. Japan 55, No. 3, 713-725 (2003).

Summary: If \(M\) is a (separable) von Neumann algebra and \(A\) is a Cartan subalgebra of \(M\), then \(M\) is determined by an equivalence relation and a 2-cocycle. By constructing an equivalence subrelation, we show that for any intermediate von Neumann subalgebra \(N\) between \(M\) and \(A\), there exists a faithful normal conditional expectation from \(M\) onto \(N\).

MSC:

46L10	General theory of von Neumann algebras
37A20	Algebraic ergodic theory, cocycles, orbit equivalence, ergodic equivalence relations

Keywords:

von Neumann algebra; Cartan subalgebra; conditional expectation