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Proceedings of the American Mathematical Society

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Regularization of semigroups that are strongly continuous for $t>0$

Author: P. C. Kunstmann
Journal: Proc. Amer. Math. Soc. 126 (1998), 2721-2724
MSC (1991): Primary 47D03, 47D06
MathSciNet review: 1473671
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Abstract: Let $E$ be a Banach space and $T:]0,\infty [\to L(E)$ a strongly continuous semigroup with $\bigcap _{t>0}\operatorname {Kern} T_t=\{0\}$. We show that the generator $A$ of $(T_t)$ generates a regularized semigroup. Our construction of a regularizing operator uses an existence result of J. Esterle.

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P. C. Kunstmann
Affiliation: Mathematisches Seminar der Universität Kiel, Ludewig-Meyn-Straße 4, D–24098 Kiel, Germany
Address at time of publication: Mathematisches Institut I der Universität Karlsruhe, Englerstraße 2, Postfach 6980, D–76128 Karlsruhe, Germany

Received by editor(s): February 7, 1997
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society