Normalizers inside amalgamated free product von Neumann algebras
Abstract
Recently, Adrian Ioana proved that all crossed products by free ergodic probability measure preserving actions of a nontrivial free product group 1 * 2 have a unique Cartan subalgebra up to unitary conjugacy. Ioana deduced this result from a more general dichotomy theorem on the normalizer NM(A)'' of an amenable subalgebra A of an amalgamated free product von Neumann algebra M = M1 *B M2. We improve this dichotomy theorem by removing the spectral gap assumptions and obtain in particular a simpler proof for the uniqueness of the Cartan subalgebra in crossed products by 1 * 2.
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