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Obstructions to the uniform stability of a \(C_{0}\)-semigroup. (English. Russian original) Zbl 1230.47075
Sib. Math. J. 51, No. 2, 330-337 (2010); translation from Sib. Mat. Zh. 51, No. 2, 410-419 (2010).
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
\[ \int_0^\infty h(|\langle x',T_tx\rangle|)\,dt=\infty. \]

MSC:
47D06 One-parameter semigroups and linear evolution equations
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