Eliminate the type I hypothesis in tensor-product strong minimality

Determine whether the assumption that the C*-algebra A is type I can be eliminated from the tensor-product strong-minimality theorem: namely, whether strongly minimal C*-flows (A,G) and (B,H) always induce a strongly minimal product C*-flow (A\otimes_{\mathrm{min}}B,G\times H) without assuming that A or B is type I.

Background

Theorem \ref{tensor-product-minimality} proves that if (A,G) and (B,H) are strongly minimal C*-flows and A is type I, then the product flow (A\otimes_{\mathrm{min}}B,G\times H) is strongly minimal. The type I hypothesis is used through a lemma asserting that product functionals are sufficiently abundant in the dual of the minimal tensor product.

The remark identifies the removal of this hypothesis as unresolved. It further explains that an affirmative answer would resolve Rørdam’s Question 7.3 by implying that the minimal tensor product of two C*-irreducible inclusions is again C*-irreducible. Conversely, an affirmative solution to that question would imply the desired tensor-product strong-minimality statement without the type I assumption.