Complete metric approximation property for $q$-Araki-Woods algebras

Abstract

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 $w^{\ast }$-complete metric approximation property for all $q$-Araki-Woods algebras. We apply the latter result to show that the canonical ultraweakly dense C${}^{\ast }$-subalgebras of $q$-Araki-Woods algebras are always QWEP.

arXiv comment24 pages

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Cited by in corpus (2)

• Full solution of the factoriality question for $q$-Araki-Woods von Neumann algebras via conjugate variables
• Connes' bicentralizer problem for q-deformed Araki-Woods algebras