Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Narutaka Ozawa

Full-text: Open access


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

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

First available in Project Euclid: 30 June 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46L10: General theory of von Neumann algebras

Maximal amenable von Neumann subalgebra free product


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.

Export citation


  • C. A. Akemann and P. A. Ostrand, Computing norms in group $C^{*}$-algebras, Amer. J. Math. 98 (1976), no. 4, 1015–1047.
  • R. Boutonnet and A. Carderi, Maximal amenable von Neumann subalgebras arising from maximal amenable subgroups, arXiv:1411.4093.
  • C. Houdayer, Gamma stability in free product von Neumann algebras, arXiv:1403.4098.
  • F. Kittaneh, Inequalities for the Schatten $p$-norm. IV, Comm. Math. Phys. 106 (1986), no. 4, 581–585.
  • S. Popa, Maximal injective subalgebras in factors associated with free groups, Adv. in Math. 50 (1983), no. 1, 27–48.