On a theorem of Rolewicz for semigroups of operators in locally convex spaces (Q1578875)
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scientific article; zbMATH DE number 1501761
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a theorem of Rolewicz for semigroups of operators in locally convex spaces |
scientific article; zbMATH DE number 1501761 |
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On a theorem of Rolewicz for semigroups of operators in locally convex spaces (English)
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30 January 2003
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\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.
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uniform exponential stability
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\(C_0\)-semigroup
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integrability condition
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