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arXiv · 1606.00808

Amenable absorption in amalgamated free product von Neumann algebras

Rémi Boutonnet·Cyril Houdayer
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Abstract

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 non normal conditional expectations.

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Rémi Boutonnet, Cyril Houdayer. 2016-06-02. Amenable absorption in amalgamated free product von Neumann algebras. https://doi.org/10.1215/21562261-2017-0030

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