Infinite products of resolvents of accretive operators - Reich, Simeon; Zaslavski, Alexander J. (Topological Methods in Nonlinear Analysis, 2000)
We study the space $\mathcal M_m$ of all $m$-accretive operators on a Banach space $X$endowed with an appropriate complete metrizable uniformity andthe 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 resolventsbecome eventually close to each other and that a generic operator in $\overline{\mathcal M}{}_m^*$ hasa unique zero and all the infinite products of its resolvents convergeuniformly on bounded subsets of $X$ to this zero.