Proceedings of the Japan Academy, Series A, Mathematical Sciences

Absence of Cartan subalgebras in continuous cores of free product von Neumann algebras

Yoshimichi Ueda

Full-text: Open access

Abstract

We show that the continuous core of any type III free product factor has no Cartan subalgebra. This is a complement to previous works due to Houdayer–Ricard and Boutonnet–Houdayer–Raum.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 90, Number 10 (2014), 151-155.

Dates
First available in Project Euclid: 4 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.pja/1417707836

Digital Object Identifier
doi:10.3792/pjaa.90.151

Mathematical Reviews number (MathSciNet)
MR3290439

Zentralblatt MATH identifier
1323.46036

Subjects
Primary: 46L54: Free probability and free operator algebras
Secondary: 46L10: General theory of von Neumann algebras

Keywords
Cartan subalgebra free product type III factor continuous core

Citation

Ueda, Yoshimichi. Absence of Cartan subalgebras in continuous cores of free product von Neumann algebras. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 10, 151--155. doi:10.3792/pjaa.90.151. https://projecteuclid.org/euclid.pja/1417707836


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References

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