Abstract:Let $T:[0, \infty ) \to L(E)$ be a $C_0$-semigroup with unbounded generator $A:D(A)\to E$. We prove that $(T(t)x-x)/t$ has generically a very irregular behaviour for $x\notin D(A)$ as $t \to 0+$.
Keywords: $C_0$-semigroups, universal elements
AMS Subject Classification: 47D06, 54H99