When is a semigroup a group?

Hans Zwart*

*Corresponding author for this work

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A well-known necessary and sufficient condition for the operator A to be the infinitesimal generator of a strongly continuous (C0) group is that both A and -A generate a C0-semigroup. This seems to imply that one has to check the conditions in the Hille-Yosida Theorem for both A and -A. In this paper we show that this is not necessary. Given that A generates a C0-semigroup we prove that a (weak) growth bound on the resolvent on a left half plane is sufficient to guarantee that A generates a group. This extends the recent result found by Liu, see [Liu98].

Original languageEnglish
Title of host publicationEuropean Control Conference, ECC 1999 - Conference Proceedings
Number of pages3
ISBN (Electronic)9783952417355
Publication statusPublished - 24 Mar 2015
Event1999 European Control Conference, ECC 1999 - Karlsruhe, Germany
Duration: 31 Aug 19993 Sep 1999


Conference1999 European Control Conference, ECC 1999
Abbreviated titleECC


  • Hilbert space
  • strongly continuous group
  • strongly continuous semigroup

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