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. 
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18 Citations

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