# ON ERGODIC AVERAGES AND THE RANGE OF A CLOSED OPERATOR

@inproceedings{Sato2006ONEA,
title={ON ERGODIC AVERAGES AND THE RANGE OF A CLOSED OPERATOR},
author={Ryotaro Sato},
year={2006}
}
For a $\gamma$-th order Ces\{a}ro mean bounded linear operator $T$ on a Banach space $X$, we characterize the range $R(A)$ of the operator $A=T-I$, by using an $A$-ergodic net and its companion net which were introduced by Dotson and developed by Shaw. Similarly, if $A$ is the generator of a $\gamma$-th order Ces\{a}ro mean bounded $C_{0}$-semigroup (or strongly continuous cosine operator function) of bounded linear operators on $X$, then we characterize the range $R(A)$.

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