Title :
When is a semigroup a group?
Author_Institution :
Fac. of Math. Sci., Univ. of Twente, Enschede, Netherlands
fDate :
Aug. 31 1999-Sept. 3 1999
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;
Conference_Titel :
Control Conference (ECC), 1999 European
Conference_Location :
Karlsruhe
Print_ISBN :
978-3-9524173-5-5
