## 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

### Keywords:

maximal amenable von Neumann subalgebra; free product

Zbl 1328.46046
Full Text:

### References:

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