Abstract. Extending former investigations on single operators with regular norm-sequences, representations of discrete abelian semigroups are studied. It is shown that if the representation exhibits ``regular'' norm-behaviour, then it can be related to an isometric representation, with useful containment properties between the corresponding spectra. As an application, a well-known stability theorem on bounded representations is extended to this general situation.

AMS Subject Classification (1991): 47D03, 47A67

Received February 5, 1999. (Registered under 2712/2009.)