Abstract

Let X be a complex Banach space, 𝒩 a norming set for X, and D⊂X a bounded, closed, and convex domain such that its norm closure D¯ is compact in σ(X,𝒩). Let ∅≠C⊂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 σ-porous.