Infinite products of holomorphic mappings

Let X be a complex Banach space, a norming setfor X, and D⊂X a bounded, closed, and convexdomain such that its norm closure D¯ is compact in σ(X,). Let ∅≠C⊂D lie strictly inside D. We study convergence properties of infiniteproducts of those self-mappings of C which can be extended toholomorphic self-mappings of D. Endowing the space of sequencesof such mappings with an appropriate metric, we show that thesubset consisting of all the sequences with divergent infiniteproducts is σ-porous