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Zeitschrift für Analysis und ihre Anwendungen


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Volume 21, Issue 4, 2002, pp. 865–878
DOI: 10.4171/ZAA/1113

Published online: 2002-12-31

The Set of Divergent Infinite Products in a Banach Space is $\sigma$-Porous

Simeon Reich[1] and Alexander J. Zaslavski[2]

(1) Technion - Israel Institute of Technology, Haifa, Israel
(2) Technion - Israel Institute of Technology, Haifa, Israel

Let $K$ be a bounded closed convex subset of a Banach space. We study several convergence properties of infinite products of non-expansive self-mappings of $K$. In our recent work we have considered several spaces of sequences of such self-mappings. Endowing them with appropriate topologies, we have shown that the infinite products corresponding to generic sequences converge. In the present paper we prove that the subsets consisting of all sequences of mappings with divergent infinite products are not only of the first Baire category, but also $\sigma$-porous.

Keywords: Complete metric space, fixed point, generic property, hyperbolic space, infinite product, non-expansive mapping, porous set

Reich Simeon, Zaslavski Alexander: The Set of Divergent Infinite Products in a Banach Space is $\sigma$-Porous. Z. Anal. Anwend. 21 (2002), 865-878. doi: 10.4171/ZAA/1113