Geodesic
A universal property of $C_0$-semigroups
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 83-88

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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 $t \to 0+$.
Classification : 47D06, 54H99
Keywords: $C_0$-semigroups; universal elements 
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     title = {A universal property of $C_0$-semigroups},
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Herzog, Gerd; Schmoeger, Christoph. A universal property of $C_0$-semigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 1, pp. 83-88. http://geodesic.mathdoc.fr/item/CMUC_2009__50_1_a6/