On a theorem of Rolewicz for semigroups of operators in locally convex spaces
\textit{R. Datko} [J. Math. Anal. Appl. 32, 610-616 (1970; Zbl 0211.16802)] characterized uniform exponential stability of \(C_0\)-semigroup \((T(t))_{t \geq 0}\) on a Banach space \(X\) by the integrability condition \(\int_0^\infty \|T(t) x\|dt < X\). This result, and its various generalizations [see \textit{J. M. A. M. v. Neerven}, ``The asymptotic behaviour of semigroups of linear operators'' (1996; Zbl 0905.47001)], is extended to semigroups on locally convex spaces.
scientific article; zbMATH DE number 1501761