Let be a II factor with a von Neumann subalgebra that has infinite index under any projection in (e.g., if is diffuse, or if is an irreducible subfactor with infinite Jones index). We prove that given any separable subalgebra of the ultrapower II factor , for a nonprincipal ultrafilter on , there exists a unitary element such that is orthogonal to .
Cite this article
Sorin Popa, Asymptotic Orthogonalization of Subalgebras in II Factors. Publ. Res. Inst. Math. Sci. 55 (2019), no. 4, pp. 795–809DOI 10.4171/PRIMS/55-4-5