Abstract. We prove that a $C_0$-semigroup $(T(s))_{s \geq0}$ with $\|T(s)\|\geq1$ $(s \geq0)$ has a regular norm-function if and only if its regularity constant is positive. This extends the characterization of single operators with regular norm-sequences.

AMS Subject Classification (1991): 47D06

Received July 30, 2008, and in final form September 4, 2008. (Registered under 6051/2009.)