2000 character limit reached
Asymptotic orthogonalization of subalgebras in II$_1$ factors (1707.07317v3)
Published 23 Jul 2017 in math.OA
Abstract: Let $M$ be a II$_1$ factor with a von Neumann subalgebra $Q\subset M$ that has infinite index under any projection in $Q'\cap M$ (e.g., $Q$ abelian; or $Q$ an irreducible subfactor with infinite Jones index). We prove that given any separable subalgebra $B$ of the ultrapower II$_1$ factor $M\omega$, for a non-principal ultrafilter $\omega$ on $\Bbb N$, there exists a unitary element $u\in M\omega$ such that $uBu*$ is orthogonal to $Q\omega$.