A remark on the ultrapower algebra of the hyperfinite factor

Chifan, Ionut; Das, Sayan

doi:10.1090/proc/14197

A remark on the ultrapower algebra of the hyperfinite factor
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by Ionut Chifan and Sayan Das PDF

Proc. Amer. Math. Soc. 146 (2018), 5289-5294 Request permission

Abstract:

On page 43 in [Adv. in Math. 50 (1983), pp. 27–48] Sorin Popa asked whether the following property holds: If $\omega$ is a free ultrafilter on $\mathbb N$ and $\mathcal {R}_1\subseteq \mathcal {R}$ is an irreducible inclusion of hyperfinite II$_1$ factors such that $\mathcal {R}’\cap \mathcal {R}^\omega \subseteq \mathcal {R}^\omega _1$ does it follows that $\mathcal {R}_1=\mathcal {R}$? In this short note we provide an affirmative answer to this question.

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