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

Received 14 September 2004

Copyright © 2005 Monika Budzyńska and Simeon Reich. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.