$\gamma $-boundedness of $C_0$-semigroups and their $H^{\infty }$-functional calculi
Volume 254 / 2020
Studia Mathematica 254 (2020), 77-108
MSC: 47A60, 47D06.
DOI: 10.4064/sm190711-30-8
Published online: 6 March 2020
Abstract
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.
