Jørgensen–Schmitt–Werner stability conjecture for Wick algebra envelopes

For a family of coefficients $T_{ij}^{kl}$, let $W(T)$ be the Wick $*$-algebra generated by $a_j,a_j^*$, and let $T\colon\mathcal H^{\otimes 2}\to\mathcal H^{\otimes 2}$ be its operator of coefficients, where $\mathcal H=\mathbb C^d$. Let $\mathcal W(T)=C^*(W(T))$ denote the universal $C^*$-envelope. Stability conjecture. If $T$ is self-adjoint, braided, and $\lVert T\rVert<1$, then

$$\mathcal W(T)\simeq\mathcal W(0).$$

The conjecture asserts that the universal $C^*$-envelope is invariant throughout this class of Wick algebras; its resolution is not specified in the supplied text.