Abstract and Applied Analysis
Volume 2005 (2005), Issue 4, Pages 327-341
Infinite products of holomorphic mappings
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.
Let be a complex Banach space, a norming set
for , and a bounded, closed, and convex
domain such that its norm closure is compact in . Let lie strictly inside . We study convergence properties of infinite
products of those self-mappings of which can be extended to
holomorphic self-mappings of . 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 -porous.