Free products of finite-dimensional and other von Neumann algebras in\n terms of free Araki-Woods factors

We show that any free product of finite-dimensional von Neumann algebras\nequipped with non-tracial states is isomorphic to a free Araki-Woods factor\nwith its free quasi-free state possibly direct sum a finite-dimensional von\nNeumann algebra. This gives a complete answer to questions posed by Dykema and\nShlyakhtenko, which had been partially answered by work of Houdayer and work of\nUeda. We also extend this to suitable infinite-dimensional von Neumann algebras\nwith almost periodic states.\n