Summation of arbitrary series by Riesz methods

It is known (theorem of Agnew and Darevskii) that for each divergent real sequence $\{s_n\}$ and each real number $c$, there exists a $T$-method of summing $\{s_n\}$ to $c$. In this note it is shown that for each divergent sequence which is bounded above or below we can take the $T$-method in the above theorem to be a Riesz method. We also study Riesz summability of unbounded (above and below) sequences.