Infinite products of resolvents of accretive operators

Simeon Reich, Alexander J. Zaslavski

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.

Keywords


Accretive operator; generic property; infinite product; uniform space

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