Extending earlier results of Datko, Pazy, and Littman on
C0-semigroups, and of
Przyluski and Weiss on operators, we prove the following. Let
T be a bounded linear operator on a Banach space
X and let
r(
T) denotes its spectral radius. Let
E be a Banach function space over N with the property that lim
n→∞![](/images/glyphs/BDK.GIF)
![](/images/glyphs/BDK.GIF)
χ
{0,...,n−1}![](/images/glyphs/BDK.GIF)
E