Infinite products of holomorphic mappings

Monika Budzyńska and Simeon Reich

Abstract and Applied Analysis, 2005, vol. 2005, issue 4, 327-341

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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https://doi.org/10.1155/AAA.2005.327

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2005:y:2005:i:4:p:327-341

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