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

Author(s): P. C. Kunstmann
Journal: Proc. Amer. Math. Soc. 126 (1998), 2721-2724.
MSC (1991): Primary 47D03, 47D06
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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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Additional Information:

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
Email: peer.kunstmann@math.uni-karlsruhe.de

DOI: 10.1090/S0002-9939-98-04636-X
PII: S 0002-9939(98)04636-X
Received by editor(s): February 7, 1997
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1998, American Mathematical Society

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