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.