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

TL;DR

This paper extends the class of contractions for second quantisation on q-Araki-Woods algebras and proves that all such algebras have the Haagerup approximation property, advancing understanding in operator algebra theory.

Contribution

It introduces an extension of the second quantisation framework for q-Araki-Woods algebras and establishes the Haagerup approximation property for all these algebras.

Findings

Extended second quantisation to a broader class of contractions.

Proved all q-Araki-Woods algebras have the Haagerup approximation property.

Enhanced the theoretical framework of operator algebras.

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.