Proceedings of the Japan Academy, Series A, Mathematical Sciences

A remark on amenable von Neumann subalgebras in a tracial free product

Narutaka Ozawa

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Abstract

We give a simple proof of a theorem of C. Houdayer that an amenable von Neumann subalgebra in a tracial free product von Neumann algebra $M=M_{1}*M_{2}$ is contained in $M_{1}$ whenever it has a diffuse intersection with $M_{1}$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 7 (2015), 104.

Dates
First available in Project Euclid: 30 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.pja/1435669942

Digital Object Identifier
doi:10.3792/pjaa.91.104

Mathematical Reviews number (MathSciNet)
MR3365404

Zentralblatt MATH identifier
1351.46059

Subjects
Primary: 46L10: General theory of von Neumann algebras

Keywords
Maximal amenable von Neumann subalgebra free product

Citation

Ozawa, Narutaka. A remark on amenable von Neumann subalgebras in a tracial free product. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 7, 104. doi:10.3792/pjaa.91.104. https://projecteuclid.org/euclid.pja/1435669942


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References

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