Abstract and Applied Analysis

Infinite products of holomorphic mappings

Monika Budzyńska and Simeon Reich

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Abstract

Let X be a complex Banach space, 𝒩 a norming set for X, and DX a bounded, closed, and convex domain such that its norm closure D¯ is compact in σ(X,𝒩). Let CD 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.

Article information

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

Dates
First available in Project Euclid: 25 July 2005

Permanent link to this document
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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