Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 327-341
doi:10.1155/AAA.2005.327
Infinite products of holomorphic mappings
Monika Budzyńska1
and Simeon Reich2
1InstytutMatematyki, UniwersytetMarii Curie-Skłodowskiej (UMCS), Lublin 20-031, Poland
2Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
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.