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.)
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