Abstract and Applied Analysis

Infinite products of holomorphic mappings

Abstract

Let $X$ be a complex Banach space, ${\mathcal{N}}$ a norming set for $X$, and $D\subset X$ a bounded, closed, and convex domain such that its norm closure $\overline{D}$ is compact in $\sigma (X,{\mathcal{N}})$. Let $\emptyset \neq C \subset D$ 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 $\sigma$-porous.

Article information

Source
Abstr. Appl. Anal., Volume 2005, Number 4 (2005), 327-341.

Dates
First available in Project Euclid: 25 July 2005

https://projecteuclid.org/euclid.aaa/1122298455

Digital Object Identifier
doi:10.1155/AAA.2005.327

Mathematical Reviews number (MathSciNet)
MR2202484

Zentralblatt MATH identifier
1115.46036

Citation

Budzyńska, Monika; Reich, Simeon. Infinite products of holomorphic mappings. Abstr. Appl. Anal. 2005 (2005), no. 4, 327--341. doi:10.1155/AAA.2005.327. https://projecteuclid.org/euclid.aaa/1122298455

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