$q$-Araki-Woods algebras: extension of second quantisation and Haagerup approximation property

Abstract

We extend the class of contractions for which the second quantisation on $q$-Araki-Woods algebras can be defined. As a corollary, we prove that all $q$-Araki-Woods algebras possess the Haagerup approximation property.

arXiv commentv2: expanded introduction, Conjecture from Section 3 is now Theorem 3.6; 10 pages