Strong Solidity of the q-Gaussian Algebras for all -1 < q < 1

TL;DR

This paper proves that q-Gaussian algebras possess the weak* CCAP and are strongly solid for all q in (-1, 1), extending understanding of their operator algebraic properties.

Contribution

It establishes the weak* CCAP and strong solidity of q-Gaussian algebras for all q in [-1, 1], including the full range of q values.

Findings

Proves weak* CCAP for all q in [-1, 1]

Shows q-Gaussian algebras are strongly solid for q in (-1, 1)

Extends previous results to the entire q-range

Abstract

The main result of this paper is to establish the weak* completely contractive approximation property (w*CCAP) for the q-Gaussian algebras for all values of q \in [-1, 1] and any number of generators. We use this to establish that the q-Gaussian algebras are strongly solid in the sense of Popa and Ozawa for q \in (-1, 1).