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A remark on the ultrapower algebra of the hyperfinite factor


Authors: Ionut Chifan and Sayan Das
Journal: Proc. Amer. Math. Soc. 146 (2018), 5289-5294
MSC (2010): Primary 46L10; Secondary 46L37
DOI: https://doi.org/10.1090/proc/14197
Published electronically: August 10, 2018
MathSciNet review: 3866868
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Abstract: On page 43 in [Adv. in Math. 50 (1983), pp. 27โ€“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 $\mathcal {R}โ€™\cap \mathcal {R}^\omega \subseteq \mathcal {R}^\omega _1$ 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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Additional Information

Ionut Chifan
Affiliation: Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242
Email: ionut-chifan@uiowa.edu

Sayan Das
Affiliation: Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, Iowa 52242
Email: sayan-das@uiowa.edu

Received by editor(s): February 19, 2018
Received by editor(s) in revised form: April 10, 2018, and April 17, 2018
Published electronically: August 10, 2018
Additional Notes: The first author was partly supported by NSF Grant DMS #1600688.
Communicated by: Adrian Ioana
Article copyright: © Copyright 2018 American Mathematical Society