Faithfulness of bi-free product states
operator algebras (math.OA), functional analysis (math.FA)
Given a non-trivial family of pairs of faces of unital C*- algebras where each pair has a faithful state, it is proved that if the bi-free product state is faithful on the reduced bi-free product of this family of pairs of faces then each pair of faces arises as a minimal tensor product. A partial converse is also obtained.
Ramsey, C. "Faithfulness of bi-free product states", Proceedings of the American Mathematical Society 146 (2018), 5279-5288. https://doi.org/10.1090/proc/14194
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