Infinite products of holomorphic mappings

Monika Budzyńska and Simeon Reich

Abstract and Applied Analysis, 2005, vol. 2005, 1-15

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.

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:740363

DOI: 10.1155/AAA.2005.327

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