JournalsprimsVol. 55, No. 4pp. 795–809

Asymptotic Orthogonalization of Subalgebras in II1_1 Factors

  • Sorin Popa

    University of California Los Angeles, USA
Asymptotic Orthogonalization of Subalgebras in II$_1$ Factors cover

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Abstract

Let MM be a II1_1 factor with a von Neumann subalgebra QMQ\subset M that has infinite index under any projection in QMQ'\cap M (e.g., if QMQ'\cap M is diffuse, or if QQ is an irreducible subfactor with infinite Jones index). We prove that given any separable subalgebra BB of the ultrapower II1_1 factor MωM^\omega, for a nonprincipal ultrafilter ω\omega on N\mathbb{N}, there exists a unitary element uMωu\in M^\omega such that uBuuBu^* is orthogonal to QωQ^\omega.

Cite this article

Sorin Popa, Asymptotic Orthogonalization of Subalgebras in II1_1 Factors. Publ. Res. Inst. Math. Sci. 55 (2019), no. 4, pp. 795–809

DOI 10.4171/PRIMS/55-4-5