• DocumentCode
    706914
  • Title

    When is a semigroup a group?

  • Author

    Zwart, Hans

  • Author_Institution
    Fac. of Math. Sci., Univ. of Twente, Enschede, Netherlands
  • fYear
    1999
  • fDate
    Aug. 31 1999-Sept. 3 1999
  • Firstpage
    3432
  • Lastpage
    3434
  • 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].
  • Keywords
    group theory; C0-semigroup; Hille-Yosida theorem; continuous group; growth bound; infinitesimal generator; left half plane; weak bound; Electronic mail; Facsimile; Generators; Hilbert space; Laplace equations; Vents; Hilbert space; strongly continuous group; strongly continuous semigroup;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Control Conference (ECC), 1999 European
  • Conference_Location
    Karlsruhe
  • Print_ISBN
    978-3-9524173-5-5
  • Type

    conf

  • Filename
    7099859
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=706914