# Is an infinitesimal generator?

Zwart, H.J.
(2007)
*Is an infinitesimal generator?*
Banach center publications, 75
.
pp. 303-313.
ISSN 0137-6934

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Abstract: | In this paper we study the question whether is the infinitesimal generator of a bounded -semigroup if generates a bounded -semigroup. If the semigroup generated by is analytic and sectorially bounded, then the same holds for the semigroup generated by . However, we construct a contraction semigroup with growth bound minus infinity for which does not generate a bounded semigroup. Using this example we construct an infinitesimal generator of a bounded semigroup for which its inverse does not generate a semigroup. Hence we show that the question posed by deLaubenfels in 1988 must be answered negatively. All these examples are on Banach spaces. On a Hilbert space the question whether the inverse of a generator of a bounded semigroup also generates a bounded semigroup still remains open. |

Item Type: | Article |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/61749 |

Official URL: | http://journals.impan.gov.pl/bc/index.html |

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