# Amenable absorption in amalgamated free product von Neumann algebras

@article{Boutonnet2016AmenableAI, title={Amenable absorption in amalgamated free product von Neumann algebras}, author={R'emi Boutonnet and Cyril Houdayer}, journal={Kyoto Journal of Mathematics}, year={2016} }

We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras M = M1 * B M2. Our main result states that under natural analytic assumptions, any amenable subalgebra of M that has a large intersection with M1 is actually contained in M1. The proof does not rely on Popa's asymptotic orthogonality property but on the study of non normal conditional expectations.

## 18 Citations

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