Complete Metric Approximation Property For Mixed $q$-Deformed Araki-Woods Factors

TL;DR

This paper proves that mixed q-deformed Araki-Woods factors possess the weak* completely metric approximation property for all symmetric matrices with entries between -1 and 1, using ultraproduct embeddings.

Contribution

It establishes the $w^*$-CMAP for mixed q-deformed Araki-Woods factors for a broad class of parameters, extending previous results.

Findings

Proves $w^*$-CMAP for all symmetric matrices with entries in (-1,1).

Uses ultraproduct embedding techniques.

Extends known approximation properties to mixed q-deformed Araki-Woods factors.

Abstract

The main result of this paper is to establish the $\text{weak}^*$ completely metric approximation property ($w^*$-CMAP) for the mixed $q$-deformed Araki-Woods factors for all symmetric matrices with entries $-1< q_{i,j}< 1$, using an ultraproduct embedding of the mixed $q$-deformed Araki-Woods factors.