-boundedness of C_0-semigroups and their H^{\infty }-functional calculi
Tom 254 / 2020
Studia Mathematica 254 (2020), 77-108
MSC: 47A60, 47D06.
DOI: 10.4064/sm190711-30-8
Opublikowany online: 6 March 2020
Streszczenie
In this article we discuss the notion of \gamma -H^{\infty }-bounded calculus, \gamma -m-H^{\infty }-bounded calculus on a half-plane and the weak-\gamma Gomilko–Shi–Feng condition and give a connection between them. Then we state a characterization of generation of a \gamma -bounded C_0-semigroup in a K-convex space, which leads to a version of Gearhart–Prüss on K-convex spaces.
