Abstract. Extending a result of S. I. Ansari and P. S. Bourdon, it is proved that supercyclic, bounded representations of discrete abelian semigroups are stable. It is shown that there are supercyclic representations consisting entirely of non-supercyclic operators. Furthermore, we obtain as a consequence that supercyclicity implies stability for strongly continuous, bounded representations of ${\msbm R}_+$, too.

AMS Subject Classification (1991): 47A16, 47A13, 47A67, 47D06

Received April 13, 2004, and in final form October 11, 2004. (Registered under 5870/2009.)