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

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**126**(1998), 2721-2724 Request permission

## 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.## References

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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
- Received by editor(s): February 7, 1997
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 2721-2724 - MSC (1991): Primary 47D03, 47D06
- DOI: https://doi.org/10.1090/S0002-9939-98-04636-X
- MathSciNet review: 1473671