Complete metric approximation property for q-Araki–Woods algebras.

By adapting an ultraproduct technique of Junge and Zeng, we prove that radial completely bounded multipliers on q -Gaussian algebras transfer to q -Araki–Woods algebras. As a consequence, we establish the w ⁎ -complete metric approximation property for all q -Araki–Woods algebras. We apply the latter result to show that the canonical ultraweakly dense C ⁎ -subalgebras of q -Araki–Woods algebras are always QWEP. [ABSTRACT FROM AUTHOR]