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In this article, we investigate a unique prime factorization property forinfinite tensor product factors. We provide several examples of type II and IIIfactors which satisfy this property, including all free product factors withdiffuse free product components. In the type III setting, this is the firstclassification result for infinite tensor product non-amenable factors. Ourproof is based on Popa's intertwining techniques and a characterization ofrelative amenability on the continuous cores.

Unique prime factorization for infinite tensor product factors