Gamma-boundedness of $C_0$-semigroups and their $H^\infty$-functional calculi

Loris Arnold

Gamma-boundedness of $C_0$-semigroups and their $H^\infty$-functional calculi

Functional Analysis 2019-07-09 v1

Authors: Loris Arnold

Abstract

We discuss the notion of $\gamma$ - $H^{\infty}$ -bounded calculus, strong $\gamma$ - $m$ - $H^{\infty}$ -bounded calculus on half-plane and weak- $\gamma$ -Gomilko-Shi-Feng condition and give a connection between them. Then we state a characterization of generation of $\gamma$ -bounded $C_0$ -semigroup in $K$ -convex space, which leads to a version of Gearhart-Pr\"uss on $K$ -convex space.

Keywords

C_0-semigroup gamma-boundedness H^infty-functional calculus K-convex space Gearhart-Prüss theorem

Cite

@article{arxiv.1907.03113,
  title  = {Gamma-boundedness of $C_0$-semigroups and their $H^\infty$-functional calculi},
  author = {Loris Arnold},
  journal= {arXiv preprint arXiv:1907.03113},
  year   = {2019}
}

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