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$\gamma $-boundedness of $C_0$-semigroups and their $H^{\infty }$-functional calculi

Volume 254 / 2020

Loris Arnold Studia Mathematica 254 (2020), 77-108 MSC: 47A60, 47D06. DOI: 10.4064/sm190711-30-8 Published online: 6 March 2020


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.


  • Loris ArnoldLaboratoire de Mathématiques de Besançon
    UMR 6623, CNRS
    Université de Franche-Comté
    25000 Besançon Cedex, France

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