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arxiv: 1606.00808 · v3 · pith:3Z6FPA2Snew · submitted 2016-06-02 · 🧮 math.OA

Amenable absorption in amalgamated free product von Neumann algebras

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keywords amenablealgebrasamalgamatedfreeneumannproductabsorptionactually
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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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