  In this article we present a new technique to obtain a lower bound for the
principal Dirichlet eigenvalue of a fully nonlinear elliptic operator. We
ilustrate the construction of an appropriate radial function required to obtain
the bound in several examples. In particular we use our results to prove that
$\lim_{p\to
\infty}\lambda_{1,p}=\lambda_{1,\infty}=\left(\frac{\pi}{2R}\right)^2$ where
$\lambda_{1,p}$ and $\lambda_{1,\infty}$ are the principal eigenvalue for the
homogeneous $p$-laplacian and the homogeneous infinity laplacian respectively.
