×

A remark on amenable von Neumann subalgebras in a tracial free product. (English) Zbl 1351.46059

Summary: We give a simple proof of a theorem of C. Houdayer [Commun. Math. Phys. 336, No. 2, 831–851 (2015; Zbl 1328.46046)] 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 \(M_1\).

MSC:

46L10 General theory of von Neumann algebras
46L09 Free products of \(C^*\)-algebras

Citations:

Zbl 1328.46046
PDFBibTeX XMLCite
Full Text: DOI arXiv Euclid

References:

[1] C. A. Akemann and P. A. Ostrand, Computing norms in group \(C^{*}\)-algebras, Amer. J. Math. 98 (1976), no. 4, 1015-1047. · Zbl 0342.22008
[2] R. Boutonnet and A. Carderi, Maximal amenable von Neumann subalgebras arising from maximal amenable subgroups, arXiv: · Zbl 1342.46055
[3] C. Houdayer, Gamma stability in free product von Neumann algebras, arXiv: · Zbl 1328.46046
[4] F. Kittaneh, Inequalities for the Schatten \(p\)-norm. IV, Comm. Math. Phys. 106 (1986), no. 4, 581-585. · Zbl 0612.47018
[5] S. Popa, Maximal injective subalgebras in factors associated with free groups, Adv. in Math. 50 (1983), no. 1, 27-48. · Zbl 0545.46041
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.