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

Loris Arnold

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arXiv · 1907.03113

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

Loris Arnold

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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.

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Loris Arnold. 2019-07-06. Gamma-boundedness of $C_0$-semigroups and their $H^\infty$-functional calculi. https://arxiv.org/abs/1907.03113

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