Amenable absorption in amalgamated free product von Neumann algebras
Copyright policy )Amenable absorption in amalgamated free product von Neumann algebras
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.
Comment: 8 pages. To appear in Kyoto J. Math
- UNIVERSITE PARIS DESCARTES France
- University of Bordeaux France
- University of Paris-Saclay France
- University of Paris France
- UNIVERSITE PARIS-SUD France
amalgamated free product von Neumann algebras, 46L10, 46L54, General theory of von Neumann algebras, Mathematics - Operator Algebras, Popa’s intertwining-by-bimodules theory, Popa's intertwining-by-bimodules theory, Free products of \(C^*\)-algebras, maximal amenable subalgebras, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], 46L10, 46L54, completely positive maps
amalgamated free product von Neumann algebras, 46L10, 46L54, General theory of von Neumann algebras, Mathematics - Operator Algebras, Popa’s intertwining-by-bimodules theory, Popa's intertwining-by-bimodules theory, Free products of \(C^*\)-algebras, maximal amenable subalgebras, [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], 46L10, 46L54, completely positive maps
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