Topological Methods in Nonlinear Analysis

Infinite products of resolvents of accretive operators

Abstract

We study the space $\mathcal M_m$ of all $m$-accretive operators on a Banach space $X$ endowed with an appropriate complete metrizable uniformity and the space $\overline{\mathcal M}{}^*_m$ which is the closure in $\mathcal M_m$ of all those operators which have a zero. We show that for a generic operator in $\mathcal M_m$ all infinite products of its resolvents become eventually close to each other and that a generic operator in $\overline{\mathcal M}{}_m^*$ has a unique zero and all the infinite products of its resolvents converge uniformly on bounded subsets of $X$ to this zero.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 15, Number 1 (2000), 153-168.

Dates
First available in Project Euclid: 22 August 2016

https://projecteuclid.org/euclid.tmna/1471873914

Mathematical Reviews number (MathSciNet)
MR1786258

Zentralblatt MATH identifier
0972.47042

Citation

Reich, Simeon; Zaslavski, Alexander J. Infinite products of resolvents of accretive operators. Topol. Methods Nonlinear Anal. 15 (2000), no. 1, 153--168. https://projecteuclid.org/euclid.tmna/1471873914

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