  It is proved that for any Dunford-Schwartz operator $T$ acting in the space
$l_\infty$ and for each $x\in c_0 $ there exists an element $\widehat x \in c_0
$ such that $\| \frac 1n \sum_{k=0}^{n-1}T^k(x) - \widehat x \|_\infty \to 0$.
