JournalszaaVol. 21, No. 4pp. 865–878

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

  • Simeon Reich

    Technion - Israel Institute of Technology, Haifa, Israel
  • Alexander J. Zaslavski

    Technion - Israel Institute of Technology, Haifa, Israel
The Set of Divergent Infinite Products in a Banach Space is $\sigma$-Porous cover
Download PDF

Abstract

Let KK be a bounded closed convex subset of a Banach space. We study several convergence properties of infinite products of non-expansive self-mappings of KK. 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 σ\sigma-porous.

Cite this article

Simeon Reich, Alexander J. Zaslavski, The Set of Divergent Infinite Products in a Banach Space is σ\sigma-Porous. Z. Anal. Anwend. 21 (2002), no. 4, pp. 865–878

DOI 10.4171/ZAA/1113