Extension of the spectral radius formulae to all linear fractional self-maps

Let $\mathcal{S}_m$ denote the class of linear fractional self-maps of the unit ball $\mathbb{B}^m$. Theorem

gives spectral radius formulae for elliptic and non-elliptic linear fractional self-maps, with the latter having dilatation coefficient $\alpha$. **Spectral radius extension conjecture.** The spectral radius formulae of Theorem

are valid for all $\varphi\in\mathcal{S}_m$.

This proposes extending the preceding spectral radius results beyond the cases established in the theorem. The supplied text does not state whether this extension has been proved or disproved.