A Julia-Wolff-Carath\'eodory theorem for infinitesimal generators in the unit ball

We prove a Julia-Wolff-Carath'edory theorem on angular derivatives of infinitesimal generators of one-parameter semigroups of holomorphic self-maps of the unit ball $B^n\subset {\mathbb{C}}^n$, starting from results recently obtained by Bracci and Shoikhet.