Abstract
We show that any free product of finite-dimensional von Neumann algebras equipped with non-tracial states is isomorphic to a free Araki–Woods factor with its free quasi-free state possibly direct sum a finite-dimensional von Neumann algebra. This gives a complete answer to questions posed by Dykema in [5] and Shlyakhtenko in [10], which had been partially answered by Houdayer in [7] and Ueda in [16]. We also extend this to suitable infinite-dimensional von Neumann algebras with almost periodic states.
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