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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
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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
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