Obstructions to the uniform stability of a \(C_{0}\)-semigroup (Q606032)
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scientific article; zbMATH DE number 5816247
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Obstructions to the uniform stability of a \(C_{0}\)-semigroup |
scientific article; zbMATH DE number 5816247 |
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Obstructions to the uniform stability of a \(C_{0}\)-semigroup (English)
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15 November 2010
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The author of the paper under review proves that, under certain conditions on a \(C_0\)-semigroup \(T_t:X\to X\), for each nondecreasing function \(h:{\mathbb R}_+\to{\mathbb R}_+\), there exist \(x\in X\) and \(x'\in X'\) such that \[ \int_0^\infty h(|\langle x',T_tx\rangle|)\,dt=\infty. \]
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exponentially stable operator semigroups
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