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Amenable absorption in amalgamated free product von Neumann algebras. (English) Zbl 1406.46045
Summary: We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $$M=M_1\ast_{B}M_{2}$$. Our main result states that, under natural analytic assumptions, any amenable subalgebra of $$M$$ that has a large intersection with $$M_{1}$$ is actually contained in $$M_{1}$$. The proof does not rely on Popa’s asymptotic orthogonality property but on the study of nonnormal conditional expectations.

##### MSC:
 46L10 General theory of von Neumann algebras 46L09 Free products of $$C^*$$-algebras
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