Let A be a simple unital C*-algebra and let B be a UHF-algebra. We prove that the group of invertible elements in A ⊗ B is dense in A ⊗ B if A is stably finite, and that A ⊗ B is purely infinite otherwise. We give (partial) results on the size of the closure of the group of invertible elements in more general simple unital C*-algebras. © 1991.
Rørdam, M. (1991). On the structure of simple C*-algebras tensored with a UHF-algebra. Journal of Functional Analysis, 100(1), 1–17. https://doi.org/10.1016/0022-1236(91)90098-P