When is a semigroup a group?

Hans Zwart*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

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
PublisherIEEE
Pages3432-3434
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

Conference

Conference1999 European Control Conference, ECC 1999
Abbreviated titleECC
CountryGermany
CityKarlsruhe
Period31/08/993/09/99

Keywords

  • Hilbert space
  • strongly continuous group
  • strongly continuous semigroup

Cite this

Zwart, H. (2015). When is a semigroup a group? In European Control Conference, ECC 1999 - Conference Proceedings (pp. 3432-3434). [7099859] IEEE.