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 \(M_1\).


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


Zbl 1328.46046
Full Text: DOI arXiv Euclid


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