### Infinite products of resolvents of accretive operators

DOI: http://dx.doi.org/10.12775/TMNA.2000.012

#### 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.

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.

#### Keywords

Accretive operator; generic property; infinite product; uniform space

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