Let $X$ be a complex Banach space, ${\mathcal{N}}$ a norming set
for $X$ , and $D\subset X$ a bounded, closed, and convex
domain such that its norm closure $\overline{D}$ is compact in $\sigma (X,{\mathcal{N}})$ . Let $\emptyset \neq C \subset D$ lie strictly inside $D$ . We study convergence properties of infinite
products of those self-mappings of $C$ which can be extended to
holomorphic self-mappings of $D$ . Endowing the space of sequences
of such mappings with an appropriate metric, we show that the
subset consisting of all the sequences with divergent infinite
products is $\sigma$ -porous.